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Maximal Cohen-Macaulay DG-complexes 最大Cohen-Macaulay dg复合物
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-02-01 Epub Date: 2026-02-04 DOI: 10.1016/j.jpaa.2026.108193
Zachary Nason
{"title":"Maximal Cohen-Macaulay DG-complexes","authors":"Zachary Nason","doi":"10.1016/j.jpaa.2026.108193","DOIUrl":"10.1016/j.jpaa.2026.108193","url":null,"abstract":"<div><div>Let <em>R</em> be a commutative noetherian local differential graded (DG) ring. In this paper we propose a definition of a maximal Cohen-Macaulay DG-complex over <em>R</em> that naturally generalizes a maximal Cohen-Macaulay complex over a noetherian local ring, as studied by Iyengar, Ma, Schwede, and Walker. Our proposed definition extends the work of Shaul on Cohen-Macaulay DG-rings and DG-modules, as any maximal Cohen-Macaulay DG-module is a maximal Cohen-Macaulay DG-complex. After proving necessary lemmas in derived commutative algebra, we establish the existence of a maximal Cohen-Macaulay DG-complex for every DG-ring with constant amplitude that admits a dualizing DG-module. We then use the existence of these DG-complexes to establish a derived Improved New Intersection Theorem for all DG-rings with constant amplitude.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108193"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174121","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}
引用次数: 0
Depth of Artin-Schreier defect towers Artin-Schreier缺陷塔深度
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-02-01 Epub Date: 2026-01-27 DOI: 10.1016/j.jpaa.2026.108184
Enric Nart , Josnei Novacoski
{"title":"Depth of Artin-Schreier defect towers","authors":"Enric Nart ,&nbsp;Josnei Novacoski","doi":"10.1016/j.jpaa.2026.108184","DOIUrl":"10.1016/j.jpaa.2026.108184","url":null,"abstract":"<div><div>The depth of a simple algebraic extension <span><math><mo>(</mo><mi>L</mi><mo>/</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on <span><math><mi>K</mi><mo>[</mo><mi>x</mi><mo>]</mo></math></span> determined by the choice of different generators of the extension. In <span><span>[11]</span></span>, we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on <span><math><mo>(</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span>, we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of <em>K</em> have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108184"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079617","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}
引用次数: 0
Equivalences in diagrammatic sets 图集中的等价
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-15 DOI: 10.1016/j.jpaa.2025.108165
Clémence Chanavat, Amar Hadzihasanovic
{"title":"Equivalences in diagrammatic sets","authors":"Clémence Chanavat,&nbsp;Amar Hadzihasanovic","doi":"10.1016/j.jpaa.2025.108165","DOIUrl":"10.1016/j.jpaa.2025.108165","url":null,"abstract":"<div><div>We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict <em>ω</em>-<!--> <!-->categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict <em>ω</em>-<!--> <!-->categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108165"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841223","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}
引用次数: 0
The second syzygy schemes of curves of large degree 第二种大次曲线的合型方案
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jpaa.2025.108148
Marian Aprodu , Andrea Bruno , Edoardo Sernesi
{"title":"The second syzygy schemes of curves of large degree","authors":"Marian Aprodu ,&nbsp;Andrea Bruno ,&nbsp;Edoardo Sernesi","doi":"10.1016/j.jpaa.2025.108148","DOIUrl":"10.1016/j.jpaa.2025.108148","url":null,"abstract":"<div><div>The present paper is a natural continuation of the previous work <span><span>[2]</span></span> where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus–<em>g</em> curve of degree at least <span><math><mn>2</mn><mi>g</mi><mo>+</mo><mn>2</mn></math></span> coincides with the curve. If the property <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> is satisfied, the equality is ensured by a more general fact emphasized in <span><span>[2]</span></span>. If <span><math><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> fails, then the analysis uses the known case of canonical curves.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108148"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705835","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}
引用次数: 0
Finding the walls for quiver moduli 求颤模的壁
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jpaa.2025.108153
Hans Franzen , Gianni Petrella , Rachel Webb
{"title":"Finding the walls for quiver moduli","authors":"Hans Franzen ,&nbsp;Gianni Petrella ,&nbsp;Rachel Webb","doi":"10.1016/j.jpaa.2025.108153","DOIUrl":"10.1016/j.jpaa.2025.108153","url":null,"abstract":"<div><div>We give an effective characterization of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108153"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885249","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}
引用次数: 0
Hall polynomials for weighted projective lines 加权投影线的霍尔多项式
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jpaa.2025.108157
Jiayi Chen , Bangming Deng , Shiquan Ruan
{"title":"Hall polynomials for weighted projective lines","authors":"Jiayi Chen ,&nbsp;Bangming Deng ,&nbsp;Shiquan Ruan","doi":"10.1016/j.jpaa.2025.108157","DOIUrl":"10.1016/j.jpaa.2025.108157","url":null,"abstract":"<div><div>This paper deals with the triangle singularity defined by the equation <span><math><mi>f</mi><mo>=</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msubsup></math></span> for a weight triple <span><math><mo>(</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>, as well as the category of coherent sheaves over the weighted projective line <span><math><mi>X</mi></math></span> defined by <em>f</em>. We calculate Hall polynomials associated with extension bundles, line bundles and torsion sheaves over <span><math><mi>X</mi></math></span>. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi (2024) <span><span>[35]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108157"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739259","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}
引用次数: 0
On the 3-Pfister number in characteristic 2 论特征2中的3-菲斯特数
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-31 DOI: 10.1016/j.jpaa.2025.108168
Ahmed Laghribi, Trisha Maiti
{"title":"On the 3-Pfister number in characteristic 2","authors":"Ahmed Laghribi,&nbsp;Trisha Maiti","doi":"10.1016/j.jpaa.2025.108168","DOIUrl":"10.1016/j.jpaa.2025.108168","url":null,"abstract":"<div><div>Let <em>F</em> be a field of characteristic 2. The <em>m</em>-Pfister number of a quadratic form <span><math><mi>φ</mi><mo>∈</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>(</mo><mi>F</mi><mo>)</mo></math></span> is the least number of forms similar to <em>m</em>-fold Pfister forms needed to express <em>φ</em> up to Witt equivalence. Our aim in this note is to discuss the case <span><math><mi>m</mi><mo>=</mo><mn>3</mn></math></span> by giving an inductive formula that explicitly bounds the 3-Pfister number of any form in <span><math><msubsup><mrow><mi>I</mi></mrow><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mi>F</mi></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108168"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926215","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}
引用次数: 0
On a Galois subcover of the Hermitian curve of genus g=18(q−1)2 g=18(q−1)2的厄米曲线的伽罗瓦子盖
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jpaa.2025.108151
Barbara Gatti , Gioia Schulte
{"title":"On a Galois subcover of the Hermitian curve of genus g=18(q−1)2","authors":"Barbara Gatti ,&nbsp;Gioia Schulte","doi":"10.1016/j.jpaa.2025.108151","DOIUrl":"10.1016/j.jpaa.2025.108151","url":null,"abstract":"<div><div>In the study of algebraic curves with many points over a finite field, a well known general problem is to understand better the properties of <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves whose genera fall in the higher part of the spectrum of the genera of all <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>-maximal curves. This problem is still open for genera smaller than <span><math><mo>⌊</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>q</mi><mo>+</mo><mn>4</mn><mo>)</mo><mo>⌋</mo></math></span>. In this paper we consider the case of <span><math><mi>g</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac><msup><mrow><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> where <span><math><mi>q</mi><mo>≡</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span> and the curve is the Galois subcover of the Hermitian curve w.r.t. a cyclic automorphism group of order 4. Our contributions concern Frobenius embedding, Weierstrass semigroups and automorphism groups.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108151"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705833","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}
引用次数: 0
Connecting affine W-algebras: A case study on sl4 连接仿射w代数：一个关于sl4的例子
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-08 DOI: 10.1016/j.jpaa.2025.108149
Justine Fasquel , Zachary Fehily , Ethan Fursman , Shigenori Nakatsuka
{"title":"Connecting affine W-algebras: A case study on sl4","authors":"Justine Fasquel ,&nbsp;Zachary Fehily ,&nbsp;Ethan Fursman ,&nbsp;Shigenori Nakatsuka","doi":"10.1016/j.jpaa.2025.108149","DOIUrl":"10.1016/j.jpaa.2025.108149","url":null,"abstract":"<div><div>We introduce a new technique to describe partial reductions and inverse Hamiltonian reductions between affine <span><math><mi>W</mi></math></span>-algebras along the closure relations of associated nilpotent orbits in the case of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, fulfilling all the missing constructions in the literature. We also apply the partial reductions to modules in the Kazhdan–Lusztig category and show compatibility with the usual reductions of Weyl modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108149"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798977","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}
引用次数: 0
The McKay conjecture with group automorphisms and the Okuyama-Wajima argument 具有群自同构的McKay猜想和Okuyama-Wajima论证
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-01-01 Epub Date: 2025-12-05 DOI: 10.1016/j.jpaa.2025.108155
Adele Maltempo , Carolina Vallejo
{"title":"The McKay conjecture with group automorphisms and the Okuyama-Wajima argument","authors":"Adele Maltempo ,&nbsp;Carolina Vallejo","doi":"10.1016/j.jpaa.2025.108155","DOIUrl":"10.1016/j.jpaa.2025.108155","url":null,"abstract":"<div><div>Let <em>N</em> be normal subgroup of a finite group <em>G</em>, <em>p</em> be a prime, <em>P</em> be a Sylow <em>p</em>-subgroup of <em>G</em> and <em>θ</em> be a <em>P</em>-invariant irreducible character of <em>N</em>. Suppose that <span><math><mi>G</mi><mo>/</mo><mi>N</mi></math></span> is a <em>p</em>-solvable group. In this note we show that, whenever a finite group <em>A</em> acts on <em>G</em> stabilizing <em>P</em>, there exists an <em>A</em>-equivariant McKay bijection between irreducible characters lying over <em>θ</em> of degree prime to <em>p</em> of <em>G</em> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>P</mi><mo>)</mo><mi>N</mi></math></span>. This is a consequence of a recent result of D. Rossi. Our approach here is independent from Rossi's and follows the original idea of the proof of the McKay conjecture for <em>p</em>-solvable groups. In particular, we rely on the so-called Okuyama-Wajima argument to deal with characters above Glauberman correspondents. For this purpose, we generalize a classical result of P. X. Gallagher on the number of irreducible characters of <em>G</em> lying over <em>θ</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108155"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145739258","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}
引用次数: 0
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