Mathematische Annalen最新文献

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">On manifolds with almost non-negative Ricci curvature and integrally-positive <ns0:math><ns0:msup><ns0:mi>k</ns0:mi> <ns0:mrow><ns0:mi>th</ns0:mi></ns0:mrow> </ns0:msup> </ns0:math> -scalar curvature.","authors":"Alessandro Cucinotta, Andrea Mondino","doi":"10.1007/s00208-026-03406-8","DOIUrl":"https://doi.org/10.1007/s00208-026-03406-8","url":null,"abstract":"<p><p>We consider manifolds with almost non-negative Ricci curvature and strictly positive integral lower bounds on the sum of the lowest <i>k</i> eigenvalues of the Ricci tensor. If <math><mrow><mo>(</mo> <msup><mi>M</mi> <mi>n</mi></msup> <mo>,</mo> <mi>g</mi> <mo>)</mo></mrow> </math> is a Riemannian manifold satisfying such curvature bounds for <math><mrow><mi>k</mi> <mo>=</mo> <mn>2</mn></mrow> </math> , then we show that <i>M</i> is contained in a neighbourhood of controlled width of an isometrically embedded 1-dimensional sub-manifold. From this, we deduce several metric and topological consequences: <i>M</i> has at most linear volume growth and at most two ends, it has bounded 1-Urysohn width, the first Betti number of <i>M</i> is bounded above by 1, and there is precise information on elements of infinite order in <math> <mrow><msub><mi>π</mi> <mn>1</mn></msub> <mrow><mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </mrow> </math> . If <math><mrow><mo>(</mo> <msup><mi>M</mi> <mi>n</mi></msup> <mo>,</mo> <mi>g</mi> <mo>)</mo></mrow> </math> is a Riemannian manifold satisfying such bounds for <math><mrow><mi>k</mi> <mo>≥</mo> <mn>2</mn></mrow> </math> , then we show that <i>M</i> has at most <math><mrow><mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> </math> -dimensional behavior at large scales. If <math><mrow><mi>k</mi> <mo>=</mo> <mi>n</mi> <mo>=</mo> <mtext>dim</mtext> <mo>(</mo> <mi>M</mi> <mo>)</mo></mrow> </math> , so that the integral lower bound is on the scalar curvature, assuming in addition that the <math><mrow><mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo></mrow> </math> -Ricci curvature is non-negative, we prove that the dimension drop at large scales improves to <math><mrow><mi>n</mi> <mo>-</mo> <mn>2</mn></mrow> </math> . From the above results we deduce topological restrictions, such as upper bounds on the first Betti number.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"394 2","pages":"49"},"PeriodicalIF":1.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12907273/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146213694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The shifted convolution problem in function fields.","authors":"Alexandra Florea, Matilde Lalín, Amita Malik, Anurag Sahay","doi":"10.1007/s00208-026-03340-9","DOIUrl":"https://doi.org/10.1007/s00208-026-03340-9","url":null,"abstract":"<p><p>We study the shifted convolution problem for the divisor function in function fields in the large degree limit, that is, the average value of <math><mrow><mi>d</mi> <mo>(</mo> <mi>f</mi> <mo>)</mo> <mi>d</mi> <mo>(</mo> <mi>f</mi> <mo>+</mo> <mi>h</mi> <mo>)</mo></mrow> </math> where <i>f</i> runs over monic polynomials in <math> <mrow><msub><mi>F</mi> <mi>q</mi></msub> <mrow><mo>[</mo> <mi>T</mi> <mo>]</mo></mrow> </mrow> </math> of a given degree, and <i>h</i> is a given monic polynomial. We prove an asymptotic formula in the range <math><mrow><mo>deg</mo> <mo>(</mo> <mi>h</mi> <mo>)</mo> <mo><</mo> <mo>(</mo> <mn>2</mn> <mo>-</mo> <mi>ϵ</mi> <mo>)</mo> <mo>deg</mo> <mo>(</mo> <mi>f</mi> <mo>)</mo></mrow> </math> . We also consider mixed correlations and self-correlations of <math> <mrow><msub><mi>r</mi> <mi>χ</mi></msub> <mo>=</mo> <mn>1</mn> <mo>⋆</mo> <mi>χ</mi></mrow> </math> , the convolution of 1 with a Dirichlet character mod <math><mi>ℓ</mi></math> , where <math><mi>ℓ</mi></math> is a monic irreducible polynomial, proving asymptotic formulae in various ranges. This includes the case of quadratic characters, which yields results about correlations of norm-counting functions of quadratic extensions of <math> <mrow><msub><mi>F</mi> <mi>q</mi></msub> <mrow><mo>[</mo> <mi>T</mi> <mo>]</mo></mrow> </mrow> </math> . A novel feature of our work is a Voronoi summation formula (equivalently, a functional equation for the Estermann function) in <math> <mrow><msub><mi>F</mi> <mi>q</mi></msub> <mrow><mo>[</mo> <mi>T</mi> <mo>]</mo></mrow> </mrow> </math> which was not previously available.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"395 1","pages":"6"},"PeriodicalIF":1.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12999764/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147499370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Positive curvature conditions on contractible manifolds.","authors":"Paul Sweeney","doi":"10.1007/s00208-026-03333-8","DOIUrl":"https://doi.org/10.1007/s00208-026-03333-8","url":null,"abstract":"<p><p>Our goal is to identify curvature conditions that distinguish Euclidean space in the case of open, contractible manifolds and the disk in the case of compact, contractible manifolds with boundary. First, we show that an open manifold that is the interior of a sufficiently connected, compact, contractible 5-manifold with boundary and supports a complete Riemannian metric with uniformly positive scalar curvature is diffeomorphic to Euclidean 5-space. Next, we investigate the analogous question for compact manifolds with boundary: Must a compact, contractible manifold that supports a Riemannian metric with positive scalar curvature and mean convex boundary necessarily be the disk? We present examples demonstrating that this curvature condition alone cannot distinguish the disk; on the other hand, we exhibit stronger curvature conditions that allow us to draw such a conclusion.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"394 3","pages":"53"},"PeriodicalIF":1.4,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12916530/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147271439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Abelian varieties of prescribed order over finite fields.","authors":"Raymond van Bommel, Edgar Costa, Wanlin Li, Bjorn Poonen, Alexander Smith","doi":"10.1007/s00208-024-03084-4","DOIUrl":"https://doi.org/10.1007/s00208-024-03084-4","url":null,"abstract":"<p><p>Given a prime power <i>q</i> and <math><mrow><mi>n</mi> <mo>≫</mo> <mn>1</mn></mrow> </math> , we prove that every integer in a large subinterval of the Hasse-Weil interval <math><mrow><mo>[</mo> <msup><mrow><mo>(</mo> <msqrt><mi>q</mi></msqrt> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> <mrow><mn>2</mn> <mi>n</mi></mrow> </msup> <mo>,</mo> <msup><mrow><mo>(</mo> <msqrt><mi>q</mi></msqrt> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> <mrow><mn>2</mn> <mi>n</mi></mrow> </msup> <mo>]</mo></mrow> </math> is <math><mrow><mo>#</mo> <mi>A</mi> <mo>(</mo> <msub><mi>F</mi> <mi>q</mi></msub> <mo>)</mo></mrow> </math> for some ordinary geometrically simple principally polarized abelian variety <i>A</i> of dimension <i>n</i> over <math><msub><mi>F</mi> <mi>q</mi></msub> </math> . As a consequence, we generalize a result of Howe and Kedlaya for <math><msub><mi>F</mi> <mn>2</mn></msub> </math> to show that for each prime power <i>q</i>, every sufficiently large positive integer is realizable, i.e., <math><mrow><mo>#</mo> <mi>A</mi> <mo>(</mo> <msub><mi>F</mi> <mi>q</mi></msub> <mo>)</mo></mrow> </math> for some abelian variety <i>A</i> over <math><msub><mi>F</mi> <mi>q</mi></msub> </math> . Our result also improves upon the best known constructions of sequences of simple abelian varieties with point counts towards the extremes of the Hasse-Weil interval. A separate argument determines, for fixed <i>n</i>, the largest subinterval of the Hasse-Weil interval consisting of realizable integers, asymptotically as <math><mrow><mi>q</mi> <mo>→</mo> <mi>∞</mi></mrow> </math> ; this gives an asymptotically optimal improvement of a 1998 theorem of DiPippo and Howe. Our methods are effective: We prove that if <math><mrow><mi>q</mi> <mo>≤</mo> <mn>5</mn></mrow> </math> , then every positive integer is realizable, and for arbitrary <i>q</i>, every positive integer <math><mrow><mo>≥</mo> <msup><mi>q</mi> <mrow><mn>3</mn> <msqrt><mi>q</mi></msqrt> <mo>log</mo> <mi>q</mi></mrow> </msup> </mrow> </math> is realizable.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 1","pages":"1167-1202"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11971235/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143795736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Median geometry for spaces with measured walls and for groups.","authors":"Indira Chatterji, Cornelia Druţu","doi":"10.1007/s00208-025-03289-1","DOIUrl":"https://doi.org/10.1007/s00208-025-03289-1","url":null,"abstract":"<p><p>We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with median geometry. The result follows from an analysis of a quasification of median geometry that provides a geometric characterization of spaces at a finite Hausdorff distance from a median space. The case of complex hyperbolic metric spaces is different; we show that these spaces cannot be at finite Hausdorff distance from a median space.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 3-4","pages":"2925-2952"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12827449/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146052861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Toponogov globalisation result for Lorentzian length spaces.","authors":"Tobias Beran, John Harvey, Lewis Napper, Felix Rott","doi":"10.1007/s00208-025-03167-w","DOIUrl":"10.1007/s00208-025-03167-w","url":null,"abstract":"<p><p>In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with lower (timelike) curvature bounds. Our approach utilises a \"cat's cradle\" construction akin to that which appears in several proofs in the metric setting. On the road to our main result, we also provide a lemma regarding the subdivision of triangles in spaces with a local lower curvature bound and a synthetic Lorentzian version of the Lebesgue Number Lemma. Several properties of time functions and the null distance on globally hyperbolic Lorentzian length spaces are also highlighted. We conclude by presenting several applications of our results, including versions of the Bonnet-Myers Theorem and the Splitting Theorem for Lorentzian length spaces with local lower curvature bounds, as well as discussion of stability of curvature bounds under Gromov-Hausdorff convergence.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3447-3478"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310883/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The wavefront set: bounds for the Langlands parameter.","authors":"Dan Ciubotaru, Ju-Lee Kim","doi":"10.1007/s00208-025-03278-4","DOIUrl":"https://doi.org/10.1007/s00208-025-03278-4","url":null,"abstract":"<p><p>For an irreducible smooth representation of a connected reductive <i>p</i>-adic group, two important associated invariants are the wavefront set and the (partly conjectural) Langlands parameter. While a wavefront set consists of <i>p</i>-adic nilpotent orbits, one constituent of the Langlands parameter is a complex nilpotent orbit in the dual Lie algebra. For unipotent representations in the sense of Lusztig, the corresponding nilpotent orbits on the two sides are related via the Lusztig-Spaltenstein duality (Ciubotaru et al. in Am J Math arXiv:2112.14354v4, J Reine Angew Math (Crelles J) 823:191-253, 2025). In this paper, we formulate a general upper-bound conjecture and several variants relating the nilpotent orbits that appear in the wavefront set and in the Langlands parameter. We also verify these expectations in some cases, including the depth-zero supercuspidal representations of classical groups and all the irreducible representations of <math><msub><mi>G</mi> <mn>2</mn></msub> </math> .</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 2","pages":"1827-1861"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559080/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolution problems with perturbed 1-Laplacian type operators on random walk spaces.","authors":"W Górny, J M Mazón, J Toledo","doi":"10.1007/s00208-025-03180-z","DOIUrl":"https://doi.org/10.1007/s00208-025-03180-z","url":null,"abstract":"<p><p>Random walk spaces are a general framework for the study of PDEs. They include as particular cases locally finite weighted connected graphs and nonlocal settings involving symmetric integrable kernels on <math> <msup><mrow><mi>R</mi></mrow> <mi>N</mi></msup> </math> . We are interested in the study of evolution problems involving two random walk structures so that the associated functionals have different growth on each structure. We also deal with the case of a functional with different growth on a partition of the random walk.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"392 3","pages":"3895-3957"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12310885/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144775719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regular logarithmic connections.","authors":"Piotr Achinger","doi":"10.1007/s00208-024-03047-9","DOIUrl":"https://doi.org/10.1007/s00208-024-03047-9","url":null,"abstract":"<p><p>We introduce the notion of a regular integrable connection on a smooth log scheme over <math><mi>C</mi></math> and construct an equivalence between the category of such connections and the category of integrable connections on its analytification, compatible with de Rham cohomology. This extends the work of Deligne (when the log structure is trivial), and combined with the work of Ogus yields a topological description of the category of regular connections in terms of certain constructible sheaves on the Kato-Nakayama space. The key ingredients are the notion of a canonical extension in this context and the existence of good compactifications of log schemes obtained recently by Włodarczyk.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"391 4","pages":"5293-5339"},"PeriodicalIF":1.3,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11954731/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143753555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups.","authors":"J Pascal Gollin, Kevin Hendrey, O-Joung Kwon, Sang-Il Oum, Youngho Yoo","doi":"10.1007/s00208-025-03293-5","DOIUrl":"https://doi.org/10.1007/s00208-025-03293-5","url":null,"abstract":"<p><p>In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs  <math><mrow><mo>(</mo> <mi>ℓ</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo></mrow> </math> of integers where such a duality holds for the family of cycles of length  <math><mi>ℓ</mi></math> modulo <i>z</i>. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"393 2","pages":"2507-2559"},"PeriodicalIF":1.4,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12559191/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145401170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}