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Duality theorem over finite fields and applications to Brauer groups 有限域上的对偶定理及其在Brauer群上的应用
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-05-01 Epub Date: 2026-01-19 DOI: 10.1016/j.jalgebra.2025.12.025
Rahul Gupta , Amalendu Krishna
{"title":"Duality theorem over finite fields and applications to Brauer groups","authors":"Rahul Gupta ,&nbsp;Amalendu Krishna","doi":"10.1016/j.jalgebra.2025.12.025","DOIUrl":"10.1016/j.jalgebra.2025.12.025","url":null,"abstract":"<div><div>We prove a duality theorem for the <em>p</em>-adic étale motivic cohomology of the complement of a divisor on a smooth projective variety over a finite field of characteristic <em>p</em>. We apply this theorem to prove several finiteness results for the Brauer group of normal surfaces and their regular loci over finite fields. In particular, we show that the Artin conjecture about the finiteness of the Brauer group for smooth projective surfaces over a finite field implies the same for all projective surfaces over the field. We also show that the Tate conjecture for divisors on smooth projective surfaces over finite fields implies its analog for normal projective surfaces over such fields.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 450-509"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025647","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
Determining unit groups and K1 of finite rings 有限环的单位群和K1的确定
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-05-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jalgebra.2026.01.019
Tommy Hofmann
{"title":"Determining unit groups and K1 of finite rings","authors":"Tommy Hofmann","doi":"10.1016/j.jalgebra.2026.01.019","DOIUrl":"10.1016/j.jalgebra.2026.01.019","url":null,"abstract":"<div><div>We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first <em>K</em>-group of finite rings.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 510-530"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025708","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
Deformations of Zappatic surfaces and their Galois covers Zappatic表面及其伽罗瓦覆盖的变形
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jalgebra.2026.01.015
Meirav Amram , Cheng Gong , Jia-Li Mo , János Kollár
{"title":"Deformations of Zappatic surfaces and their Galois covers","authors":"Meirav Amram ,&nbsp;Cheng Gong ,&nbsp;Jia-Li Mo ,&nbsp;János Kollár","doi":"10.1016/j.jalgebra.2026.01.015","DOIUrl":"10.1016/j.jalgebra.2026.01.015","url":null,"abstract":"<div><div>This paper considers some algebraic surfaces that can deform to planar Zappatic surfaces with a unique singularity of type <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. We prove that the Galois covers of these surfaces are all simply connected of general type, for <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. We also give a formula for a local Zappatic singularity of a Zappatic surface of type <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. As an application, we prove that such surfaces do not exist for <span><math><mi>n</mi><mo>&gt;</mo><mn>30</mn></math></span>. Furthermore, Kollár improves the result to <span><math><mi>n</mi><mo>&gt;</mo><mn>9</mn></math></span> in Appendix <span><span>A</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"693 ","pages":"Pages 710-731"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075492","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
Tensor products of infinite-dimensional evaluation modules over the Yangian Y(sl2) Yangian Y（sl2）上无限维评价模的张量积
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2026-01-07 DOI: 10.1016/j.jalgebra.2026.01.001
Hongjia Chen , Han Dai , Xingpeng Liu , Qi Zhao
{"title":"Tensor products of infinite-dimensional evaluation modules over the Yangian Y(sl2)","authors":"Hongjia Chen ,&nbsp;Han Dai ,&nbsp;Xingpeng Liu ,&nbsp;Qi Zhao","doi":"10.1016/j.jalgebra.2026.01.001","DOIUrl":"10.1016/j.jalgebra.2026.01.001","url":null,"abstract":"<div><div>We establish a necessary and sufficient condition for the tensor product <span><math><mi>W</mi><mo>=</mo><mi>M</mi><msub><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>M</mi><msub><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>)</mo></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow></msub></math></span> to be cyclic (i.e., generated by the tensor product of the highest weight vectors), where <span><math><mi>M</mi><msub><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></math></span> denotes the evaluation module of <span><math><mi>Y</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> obtained by the Verma module <span><math><mi>M</mi><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math></span> of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> via the evaluation homomorphism. When <em>W</em> is cyclic, its generators and relations can be described. Moreover, by extending it, we define a class of highest weight modules, all of which belong to the category <span><math><mi>O</mi><mo>(</mo><mi>Y</mi><mo>(</mo><msub><mrow><mi>sl</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>)</mo></math></span>. Additionally, we determine the simplicity of these modules and offer a cyclicity criterion for their tensor products.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 627-652"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978454","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 infinitude of locally 9-arc-transitive graphs 局部9弧传递图的无穷性
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2026-01-05 DOI: 10.1016/j.jalgebra.2025.11.033
Marston D.E. Conder
{"title":"The infinitude of locally 9-arc-transitive graphs","authors":"Marston D.E. Conder","doi":"10.1016/j.jalgebra.2025.11.033","DOIUrl":"10.1016/j.jalgebra.2025.11.033","url":null,"abstract":"<div><div>A graph Γ is called <em>locally s-arc-transitive</em> if the stabiliser in <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> of a vertex <em>v</em> is transitive on the set of all <em>r</em>-arcs in Γ with initial vertex <em>v</em>, for every <span><math><mi>r</mi><mo>≤</mo><mi>s</mi></math></span>. A theorem by Stellmacher and van Bon (2015) states that if Γ is a connected finite locally <em>s</em>-arc-transitive graph in which every vertex has valency at least 3, then <span><math><mi>s</mi><mo>≤</mo><mn>9</mn></math></span>. This theorem complements Tutte's famous theorem for <em>s</em>-arc-transitive finite graphs of valency 3 (showing that <span><math><mi>s</mi><mo>≤</mo><mn>5</mn></math></span>) and its extension by Weiss to <em>s</em>-arc-transitive finite graphs of higher valency (for which <span><math><mi>s</mi><mo>≤</mo><mn>7</mn></math></span>). In the current paper, the author gives a positive answer to a question by Michael Giudici, by showing that locally 9-arc-transitive graphs are not as rare as might have been expected. Specifically, it is proved that for all but finitely many <em>n</em>, there exists a finite graph upon which the alternating group <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> acts as a locally 9-arc-transitive group of automorphisms. The proof involves the construction and combination of finite quotients of an amalgamated product <span><math><mi>A</mi><msub><mrow><mo>⁎</mo></mrow><mrow><mi>C</mi></mrow></msub><mi>B</mi></math></span> where <em>A</em> and <em>B</em> are vertex-stabilisers of orders 12288 and 20480 intersecting in an edge-stabiliser of order 4096.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 582-591"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978452","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
Fractional Brauer configuration algebras I: Definitions and examples 分数阶布劳尔组形代数I：定义和例子
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2025-12-16 DOI: 10.1016/j.jalgebra.2025.12.011
Nengqun Li , Yuming Liu
{"title":"Fractional Brauer configuration algebras I: Definitions and examples","authors":"Nengqun Li ,&nbsp;Yuming Liu","doi":"10.1016/j.jalgebra.2025.12.011","DOIUrl":"10.1016/j.jalgebra.2025.12.011","url":null,"abstract":"<div><div>In 2017, Green and Schroll introduced a generalization of Brauer graph algebras which they call Brauer configuration algebras. In the present paper, we further generalize Brauer configuration algebras to fractional Brauer configuration algebras by generalizing Brauer configurations to fractional Brauer configurations. The fractional Brauer configuration algebras are locally bounded but neither finite-dimensional nor symmetric in general. We show that if the fractional Brauer configuration is of type S (resp. of type MS), then the corresponding fractional Brauer configuration algebra is a locally bounded Frobenius algebra (resp. a locally bounded special multiserial Frobenius algebra). Moreover, we show that over an algebraically closed field, the class of finite-dimensional indecomposable representation-finite fractional Brauer configuration algebras in type S coincides with the class of basic indecomposable finite-dimensional standard representation-finite self-injective algebras.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 336-378"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837887","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
Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases Cohen-Macaulay， Gorenstein和完全交叉条件由标记基
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2026-01-05 DOI: 10.1016/j.jalgebra.2025.11.034
Cristina Bertone , Francesca Cioffi , Matthias Orth , Werner M. Seiler
{"title":"Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases","authors":"Cristina Bertone ,&nbsp;Francesca Cioffi ,&nbsp;Matthias Orth ,&nbsp;Werner M. Seiler","doi":"10.1016/j.jalgebra.2025.11.034","DOIUrl":"10.1016/j.jalgebra.2025.11.034","url":null,"abstract":"<div><div>Using techniques from the theory of marked bases, we develop new effective methods for detecting and constructing Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals over a field <span><math><mi>K</mi></math></span>. Due to the functorial properties of marked bases, an elementary proof follows for the openness of the arithmetically Cohen-Macaulay, arithmetically Gorenstein and strict complete intersection <span><math><mi>K</mi></math></span>-rational points loci in a Hilbert scheme with a non-constant Hilbert polynomial.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 550-581"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939131","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
Classification of restricted Lie algebras of dimension 4 4维受限李代数的分类
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2025-12-12 DOI: 10.1016/j.jalgebra.2025.12.013
W. Liu, G.-S. Zhou
{"title":"Classification of restricted Lie algebras of dimension 4","authors":"W. Liu,&nbsp;G.-S. Zhou","doi":"10.1016/j.jalgebra.2025.12.013","DOIUrl":"10.1016/j.jalgebra.2025.12.013","url":null,"abstract":"<div><div>Restricted Lie algebras of dimension up to 3 over algebraically closed fields of positive characteristic were classified by Wang and his collaborators in <span><span>[25]</span></span>, <span><span>[19]</span></span>. In this paper, we obtain a classification of restricted Lie algebras of dimension 4 over such fields.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 271-316"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798824","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
Ordinary and modular properties of twisted Foulkes modules 扭曲Foulkes模的普通和模性质
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2026-01-05 DOI: 10.1016/j.jalgebra.2025.11.035
Josh Hall, Aparna Upadhyay
{"title":"Ordinary and modular properties of twisted Foulkes modules","authors":"Josh Hall,&nbsp;Aparna Upadhyay","doi":"10.1016/j.jalgebra.2025.11.035","DOIUrl":"10.1016/j.jalgebra.2025.11.035","url":null,"abstract":"<div><div>The action of the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></msub></math></span> on set partitions of a set of size 2<em>m</em> into <em>m</em> sets each of size 2 generates the Foulkes module <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow></msup></math></span>. In this paper, we study both the ordinary and the modular structure of the twisted Foulkes module <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup><mo>;</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> of the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, where <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>m</mi><mo>+</mo><mi>k</mi></math></span>, defined over a field. Over characteristic zero, we construct a polynomial whose coefficients are the ordinary characters of the various twisted Foulkes modules of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> as <em>m</em> and <em>k</em> vary. Further, when the underlying field has odd characteristic, we study the asymptotics of the non-projective part of the tensor powers of these modules by computing the gamma invariant as defined by Dave Benson and Peter Symonds.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 484-518"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939129","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
Frobenius functors and Gorenstein objects with applications to the flat-cotorsion theory Frobenius函子和Gorenstein对象及其在平扭理论中的应用
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2026-04-15 Epub Date: 2025-12-31 DOI: 10.1016/j.jalgebra.2025.12.018
Li Liang , Yajun Ma
{"title":"Frobenius functors and Gorenstein objects with applications to the flat-cotorsion theory","authors":"Li Liang ,&nbsp;Yajun Ma","doi":"10.1016/j.jalgebra.2025.12.018","DOIUrl":"10.1016/j.jalgebra.2025.12.018","url":null,"abstract":"<div><div>We prove that under some mild conditions, each faithful Frobenius functor preserves and reflects right <span><math><mi>U</mi></math></span>-Gorenstein objects and further preserves the right <span><math><mi>U</mi></math></span>-Gorenstein dimension of unbounded complexes, where <span><math><mi>U</mi></math></span> is the left part of a right periodic cotorsion pair. Consequently, such functors preserve and reflect Gorenstein flat-cotorsion modules. As an application, we show that the Gorenstein flat-cotorsion property of module factorizations and <span><math><mi>Q</mi></math></span>-shaped diagrams has a “local-global” principle. Finally, we study the behavior of relative stable categories, singularity categories and Gorenstein defect categories under Frobenius functors.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"692 ","pages":"Pages 463-483"},"PeriodicalIF":0.8,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939127","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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