Journal of Pure and Applied Algebra最新文献

{"title":"Interpolation in weighted projective spaces","authors":"Shahriyar Roshan Zamir","doi":"10.1016/j.jpaa.2025.108167","DOIUrl":"10.1016/j.jpaa.2025.108167","url":null,"abstract":"<div><div>Over an algebraically closed field, the <em>double point interpolation</em> problem asks for the vector space dimension of the projective hypersurfaces of degree <em>d</em> singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992–1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this paper we primarily use commutative algebra to lay the groundwork necessary to prove analogous statements in the <em>weighted projective space</em>, a natural generalization of the projective space. We prove the Hilbert function of general simple points in any <em>n</em>-dimensional weighted projective space exhibits the expected behavior. We also introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108167"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral flow equivariance for Calabi-Yau Sigma models","authors":"Emile Bouaziz","doi":"10.1016/j.jpaa.2025.108156","DOIUrl":"10.1016/j.jpaa.2025.108156","url":null,"abstract":"<div><div>We write down an explicit operator on the chiral de Rham complex of a Calabi-Yau variety <em>X</em> which intertwines the usual <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> module structure with its twist by the spectral flow automorphism of the <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>, producing the expected <em>spectral flow equivariance</em>. Taking the trace of the operators <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>J</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> on cohomology, and using the obvious interaction of spectral flow with characters, we obtain an explicit categorification of ellipticity of the elliptic genus of <em>X</em>, which is well known by other means.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108156"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradings on nilpotent Lie algebras associated with the nilpotent fundamental groups of smooth complex algebraic varieties","authors":"Taito Shimoji","doi":"10.1016/j.jpaa.2025.108154","DOIUrl":"10.1016/j.jpaa.2025.108154","url":null,"abstract":"<div><div>Let Γ be a lattice in a simply-connected nilpotent Lie group <em>N</em> whose Lie algebra <span><math><mi>n</mi></math></span> is <em>p</em>-filiform. We show that Γ is either abelian or 2-step nilpotent if Γ is isomorphic to the fundamental group of a smooth complex algebraic variety. Moreover as an application of our result, we give a required condition of a lattice in a simply-connected nilpotent Lie group of dimension less than or equal to six to be isomorphic to the fundamental group of a smooth complex algebraic variety.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108154"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On certain root number 1 cases of the cube sum problem","authors":"Shamik Das,&nbsp;Somnath Jha","doi":"10.1016/j.jpaa.2025.108145","DOIUrl":"10.1016/j.jpaa.2025.108145","url":null,"abstract":"<div><div>We consider certain families of integers <em>n</em> determined by some congruence condition, such that the global root number of the elliptic curve <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub><mo>:</mo><msup><mrow><mi>Y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is 1 for every <em>n</em>, however a given <em>n</em> may or may not be a sum of two rational cubes. We give explicit criteria in terms of the 2-parts and 3-parts of the ideal class groups of certain cubic number fields to determine whether such an <em>n</em> is a cube sum. In particular, we study integers <em>n</em> divisible by 3 such that the global root number of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> is 1. For example, for a prime <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, we show that for 3<em>ℓ</em> to be a sum of two rational cubes, it is necessary that the ideal class group of <span><math><mi>Q</mi><mo>(</mo><mroot><mrow><mn>12</mn><mi>ℓ</mi></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></math></span> contains <span><math><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>6</mn><mi>Z</mi></mrow></mfrac><mo>⊕</mo><mfrac><mrow><mi>Z</mi></mrow><mrow><mn>3</mn><mi>Z</mi></mrow></mfrac></math></span> as a subgroup. Moreover, for a positive proportion of primes <span><math><mi>ℓ</mi><mo>≡</mo><mn>7</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>9</mn><mo>)</mo></math></span>, 3<em>ℓ</em> can not be a sum of two rational cubes. A key ingredient in the proof is to explore the relation between the 2-Selmer group and the 3-isogeny Selmer group of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mo>−</mo><mn>432</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> with the ideal class groups of appropriate cubic number fields.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108145"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the ext analog of the Euler characteristic","authors":"Benjamin Katz,&nbsp;Andrew J. Soto Levins","doi":"10.1016/j.jpaa.2025.108152","DOIUrl":"10.1016/j.jpaa.2025.108152","url":null,"abstract":"<div><div>This work concerns an Ext analog of the classical Euler characteristic of a pair of finitely generated modules over commutative noetherian local rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108152"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The derived ∞-category of Cartier modules","authors":"Klaus Mattis,&nbsp;Timo Weiß","doi":"10.1016/j.jpaa.2025.108150","DOIUrl":"10.1016/j.jpaa.2025.108150","url":null,"abstract":"<div><div>For an endofunctor <span><math><mi>F</mi><mo>:</mo><mi>C</mi><mo>→</mo><mi>C</mi></math></span> on an (∞-)category <span><math><mi>C</mi></math></span> we define the ∞-category <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> of generalized Cartier modules as the lax equalizer of <em>F</em> and the identity. This generalizes the notion of Cartier modules on <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-schemes considered in <span><span>[4]</span></span>. We show that in favorable cases <span><math><mi>Cart</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> is monadic over <span><math><mi>C</mi></math></span>. If <span><math><mi>A</mi></math></span> is a Grothendieck abelian category and <span><math><mi>F</mi><mo>:</mo><mi>A</mi><mo>→</mo><mi>A</mi></math></span> is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>F</mi><mo>)</mo><mo>)</mo><mo>≃</mo><mi>Cart</mi><mo>(</mo><mi>D</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mi>D</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>)</mo></math></span> of stable ∞-categories. We use this equivalence to construct a perverse t-structure on <span><math><mi>D</mi><mo>(</mo><mi>Cart</mi><mo>(</mo><mi>Mod</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>F</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>)</mo><mo>)</mo></math></span> for any Noetherian <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-scheme <em>X</em> with absolute Frobenius <em>F</em>. If <em>F</em> is finite, this coincides with the perverse t-structure constructed in <span><span>[3]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108150"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Consistent varieties and their complete motivic decompositions","authors":"Nikita A. Karpenko","doi":"10.1016/j.jpaa.2025.108166","DOIUrl":"10.1016/j.jpaa.2025.108166","url":null,"abstract":"<div><div>Given a reductive algebraic group <em>G</em>, we introduce a notion of <em>consistent</em> projective <em>G</em>-homogeneous variety <em>X</em>. For instance, the variety of Borel subgroups in <em>G</em> is consistent; if <em>G</em> is of inner type, all projective <em>G</em>-homogeneous varieties are consistent.</div><div>Our main result describes the summands in the complete motivic decomposition of <em>X</em>. It extends an earlier result of the author providing the same for <em>G</em> of inner type.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108166"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dagger groups and p-adic distribution algebras","authors":"Aranya Lahiri ,&nbsp;Claus Sorensen ,&nbsp;Matthias Strauch","doi":"10.1016/j.jpaa.2025.108147","DOIUrl":"10.1016/j.jpaa.2025.108147","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> be a <em>p</em>-saturated group and <span><math><mi>K</mi><mo>/</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> a complete and discretely valued extension. In this paper we introduce the space of <em>K</em>-valued <em>overconvergent</em> functions <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>. In the process we promote the rigid analytic group attached to <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> in <span><span>[13]</span></span> to a dagger group. A main result of this article is that under certain assumptions (satisfied for example when <em>G</em> is a uniform pro-<em>p</em> group) the distribution algebra <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, i.e. the strong dual of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>, is a Fréchet-Stein algebra in the sense of <span><span>[21]</span></span>.</div><div>In the last section we introduce overconvergent representations and show that there is an anti-equivalence of categories between overconvergent <em>G</em>-representations of compact type and continuous <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>†</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>,</mo><mi>K</mi><mo>)</mo></math></span>-modules on nuclear Fréchet spaces. This is analogous to the anti-equivalence between locally analytic representations and modules over the locally analytic distribution algebra as proved in <span><span>[20]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108147"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"All hyperbolic cyclically presented groups with positive length three relators","authors":"Ihechukwu Chinyere ,&nbsp;Martin Edjvet ,&nbsp;Gerald Williams","doi":"10.1016/j.jpaa.2025.108133","DOIUrl":"10.1016/j.jpaa.2025.108133","url":null,"abstract":"<div><div>We consider the cyclically presented groups defined by cyclic presentations with 2<em>m</em> generators <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> whose relators are the 2<em>m</em> positive length three relators <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi><mo>+</mo><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>. We show that they are hyperbolic if and only if <span><math><mi>m</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>}</mo></math></span>. This completes the classification of the hyperbolic cyclically presented groups with positive length three relators.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108133"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enveloping operads and applications","authors":"Victor Carmona","doi":"10.1016/j.jpaa.2025.108119","DOIUrl":"10.1016/j.jpaa.2025.108119","url":null,"abstract":"<div><div>This work addresses the homotopical analysis of enveloping operads in a general cofibrantly generated symmetric monoidal model category. We show the potential of this analysis by obtaining, in a uniform way, several central results regarding the homotopy theory of operadic algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108119"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145384599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}