Compositio Mathematica最新文献

{"title":"Zeros of Rankin–Selberg L-functions in families","authors":"Peter Humphries, Jesse Thorner","doi":"10.1112/s0010437x24007085","DOIUrl":"https://doi.org/10.1112/s0010437x24007085","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {F}_n$</span></span></img></span></span> be the set of all cuspidal automorphic representations <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$pi$</span></span></img></span></span> of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathrm {GL}_n$</span></span></img></span></span> with unitary central character over a number field <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$F$</span></span></img></span></span>. We prove the first unconditional zero density estimate for the set <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal {S}={L(s,pi times pi ')colon pi in mathfrak {F}_n}$</span></span></img></span></span> of Rankin–Selberg <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$L$</span></span></img></span></span>-functions, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$pi 'in mathfrak {F}_{n'}$</span></span></img></span></span> is fixed. We use this density estimate to establish: (i) a hybrid-aspect subconvexity bound at <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$s=frac {1}{2}$</span></span></img></span></span> for almost all <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240402192832797-0216:S0010437X24007085:S0010437X24007085_inline10.png\"><span data-mathjax-type=\"texmath\"><span>$L(s,pi times pi ')in mathcal {S}$</span></","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"40 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140561430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fields of moduli and the arithmetic of tame quotient singularities","authors":"Giulio Bresciani, Angelo Vistoli","doi":"10.1112/s0010437x2400705x","DOIUrl":"https://doi.org/10.1112/s0010437x2400705x","url":null,"abstract":"<p>Given a perfect field <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$k$</span></span></img></span></span> with algebraic closure <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$overline {k}$</span></span></img></span></span> and a variety <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$overline {k}$</span></span></img></span></span>, the field of moduli of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> is the subfield of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$overline {k}$</span></span></img></span></span> of elements fixed by field automorphisms <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$gamma in operatorname {Gal}(overline {k}/k)$</span></span></img></span></span> such that the Galois conjugate <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$X_{gamma }$</span></span></img></span></span> is isomorphic to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240326174202036-0722:S0010437X2400705X:S0010437X2400705X_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span>. The field of moduli is contained in all subextensions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambri","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"158 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modular curves and Néron models of generalized Jacobians","authors":"Bruce W. Jordan, Kenneth A. Ribet, Anthony J. Scholl","doi":"10.1112/s0010437x23007662","DOIUrl":"https://doi.org/10.1112/s0010437x23007662","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$R$</span></span></img></span></span>, and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {m}$</span></span></img></span></span> a modulus on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span>, given by a closed subscheme of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> which is geometrically reduced. The generalized Jacobian <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$J_mathfrak {m}$</span></span></img></span></span> of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> with respect to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$mathfrak {m}$</span></span></img></span></span> is then an extension of the Jacobian of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240325174228573-0602:S0010437X23007662:S0010437X23007662_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$X$</span></span></img></span></span> by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular m","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"75 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The analytic classification of plane curves","authors":"Marcelo Escudeiro Hernandes, Maria Elenice Rodrigues Hernandes","doi":"10.1112/s0010437x24007061","DOIUrl":"https://doi.org/10.1112/s0010437x24007061","url":null,"abstract":"<p>In this paper, we present a solution to the problem of the analytic classification of germs of plane curves with several irreducible components. Our algebraic approach follows precursive ideas of Oscar Zariski and as a subproduct allows us to recover some particular cases found in the literature.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"19 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140170758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrepancy of rational points in simple algebraic groups","authors":"Alexander Gorodnik, Amos Nevo","doi":"10.1112/s0010437x23007716","DOIUrl":"https://doi.org/10.1112/s0010437x23007716","url":null,"abstract":"<p>The aim of the present paper is to derive effective discrepancy estimates for the distribution of rational points on general semisimple algebraic group varieties, in general families of subsets and at arbitrarily small scales. We establish mean-square, almost sure and uniform estimates for the discrepancy with explicit error bounds. We also prove an analogue of W. Schmidt's theorem, which establishes effective almost sure asymptotic counting of rational solutions to Diophantine inequalities in the Euclidean space. We formulate and prove a version of it for rational points on the group variety, with an effective bound which in some instances can be expected to be the best possible.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"116 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convexity of multiplicities of filtrations on local rings","authors":"Harold Blum, Yuchen Liu, Lu Qi","doi":"10.1112/s0010437x23007972","DOIUrl":"https://doi.org/10.1112/s0010437x23007972","url":null,"abstract":"<p>We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a consequence, we prove that the volume of a valuation is log convex on simplices of quasi-monomial valuations and give a new proof of a theorem of Xu and Zhuang on the uniqueness of normalized volume minimizers. In another direction, we generalize a theorem of Rees on multiplicities of ideals to filtrations and characterize when the Minkowski inequality for filtrations is an equality under mild assumptions.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"27 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140117466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constructing abelian varieties from rank 2 Galois representations","authors":"Raju Krishnamoorthy, Jinbang Yang, Kang Zuo","doi":"10.1112/s0010437x23007728","DOIUrl":"https://doi.org/10.1112/s0010437x23007728","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline1.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$U$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; be a smooth affine curve over a number field &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$K$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; with a compactification &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$X$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; and let &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;${mathbb {L}}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; be a rank &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline5.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$2$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, geometrically irreducible lisse &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline6.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$overline {{mathbb {Q}}}_ell$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;-sheaf on &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline7.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$U$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; with cyclotomic determinant that extends to an integral model, has Frobenius traces all in some fixed number field &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline8.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$Esubset overline {mathbb {Q}}_{ell }$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, and has bad, infinite reduction at some closed point &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307072459819-0092:S0010437X23007728:S0010437X23007728_inline9.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$x$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"2676 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140053721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"There are at most finitely many singular moduli that are S-units","authors":"Sebastián Herrero, Ricardo Menares, Juan Rivera-Letelier","doi":"10.1112/s0010437x23007704","DOIUrl":"https://doi.org/10.1112/s0010437x23007704","url":null,"abstract":"<p>We show that for every finite set of prime numbers <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304200415819-0744:S0010437X23007704:S0010437X23007704_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$S$</span></span></img></span></span>, there are at most finitely many singular moduli that are <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304200415819-0744:S0010437X23007704:S0010437X23007704_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$S$</span></span></img></span></span>-units. The key new ingredient is that for every prime number <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304200415819-0744:S0010437X23007704:S0010437X23007704_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$p$</span></span></img></span></span>, singular moduli are <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304200415819-0744:S0010437X23007704:S0010437X23007704_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$p$</span></span></img></span></span>-adically disperse. We prove analogous results for the Weber modular functions, the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304200415819-0744:S0010437X23007704:S0010437X23007704_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$lambda$</span></span></img></span></span>-invariants and the McKay–Thompson series associated with the elements of the monster group. Finally, we also obtain that a modular function that specializes to infinitely many algebraic units at quadratic imaginary numbers must be a weak modular unit.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"156 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Hasse principle for complete intersections","authors":"Matthew Northey, Pankaj Vishe","doi":"10.1112/s0010437x23007698","DOIUrl":"https://doi.org/10.1112/s0010437x23007698","url":null,"abstract":"<p>We prove the Hasse principle for a smooth projective variety <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$Xsubset mathbb {P}^{n-1}_mathbb {Q}$</span></span></img></span></span> defined by a system of two cubic forms <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$F,G$</span></span></img></span></span> as long as <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$ngeq 39$</span></span></img></span></span>. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Q}$</span></span></img></span></span>.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"28 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On straightening for Segal spaces","authors":"Joost Nuiten","doi":"10.1112/s0010437x23007674","DOIUrl":"https://doi.org/10.1112/s0010437x23007674","url":null,"abstract":"<p>The straightening–unstraightening correspondence of Grothendieck–Lurie provides an equivalence between cocartesian fibrations between <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240222174850284-0238:S0010437X23007674:S0010437X23007674_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$(infty, 1)$</span></span></img></span></span>-categories and diagrams of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240222174850284-0238:S0010437X23007674:S0010437X23007674_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(infty, 1)$</span></span></img></span></span>-categories. We provide an alternative proof of this correspondence, as well as an extension of straightening–unstraightening to all higher categorical dimensions. This is based on an explicit combinatorial result relating two types of fibrations between double categories, which can be applied inductively to construct the straightening of a cocartesian fibration between higher categories.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":"276 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139948376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}