Journal of Algebra最新文献

{"title":"Instanton sheaves on ruled Fano 3-folds of Picard rank 2 and index 1","authors":"Ozhan Genc ,&nbsp;Marcos Jardim","doi":"10.1016/j.jalgebra.2025.07.051","DOIUrl":"10.1016/j.jalgebra.2025.07.051","url":null,"abstract":"<div><div>We study rank 2 <em>h</em>-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free <em>h</em>-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free <em>h</em>-instanton sheaf. Our focus then shifts to ruled Fano threefolds of Picard rank 2 and index 1, of which there are five deformation classes. We establish the existence of orientable rank 2 <em>h</em>-instanton bundles on such varieties. Additionally, we prove the existence of Ulrich bundles on such varieties, which correspond to <em>h</em>-instanton sheaves of minimum charge.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 579-607"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865980","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":"Logarithmic Hochschild co/homology via formality of derived intersections","authors":"Márton Hablicsek ,&nbsp;Leo Herr ,&nbsp;Francesca Leonardi","doi":"10.1016/j.jalgebra.2025.07.048","DOIUrl":"10.1016/j.jalgebra.2025.07.048","url":null,"abstract":"<div><div>We define log Hochschild co/homology for log schemes that behaves well for simple normal crossing pairs <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> or toroidal singularities.</div><div>We prove a Hochschild-Kostant-Rosenberg isomorphism for log smooth schemes, as well as an equivariant version for log orbifolds. We define cyclic homology and compute it in simple cases. We show that log Hochschild co/homology is invariant under log alterations.</div><div>Our main technical result in log geometry shows the tropicalization (Artin fan) of a product of log schemes <span><math><mi>X</mi><mo>×</mo><mi>Y</mi></math></span> is usually the product of the tropicalizations of <em>X</em> and <em>Y</em>. This and the machinery of <em>formality</em> of derived intersections facilitate a geometric approach to log Hochschild.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"686 ","pages":"Pages 127-175"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902156","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":"Representation of partially ordered sets over Von Neumann regular algebras. More prime, non-primitive regular rings","authors":"Giuseppe Baccella","doi":"10.1016/j.jalgebra.2025.08.005","DOIUrl":"10.1016/j.jalgebra.2025.08.005","url":null,"abstract":"<div><div>Given an <em>infinite</em> cardinal <strong>ℵ</strong>, let <span><math><mi>P</mi><mi>o</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ℵ</mi></mrow></msub></math></span> be the category whose objects are all partially ordered sets <em>I</em>, having a finite cofinal subset and such that both <em>I</em> and the set of all maximal chains of <em>I</em> have at most cardinality <strong>ℵ</strong>, while the morphisms are all maps which are order imbeddings of the domain as an upper subset of the codomain. Given a field <span><math><mi>K</mi></math></span>, for every object <em>I</em> of <span><math><mi>P</mi><mi>o</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ℵ</mi></mrow></msub></math></span> we find a unital, locally matricial and hence unit-regular <span><math><mi>K</mi></math></span>-algebra <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> such that the lattice of all its ideals is order isomorphic to the lattice of all lower subsets of <em>I</em>. We show that the Grothendieck group <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo><mo>)</mo></math></span>, with its natural partial order, is order isomorphic to the restricted Hahn power of <span><math><mi>Z</mi></math></span> by <em>I</em>; this gives a contribution to solve the <em>Realization Problem for Dimension Groups with order-unit</em>. We also show that the algebra <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> has the following features: (a) <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> is prime if and only if <em>I</em> is lower directed; (b) <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> is primitive if and only if <em>I</em> has a coinitial chain; (c) <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> is semiartinian if and only if <em>I</em> is artinian, in which case <em>I</em> is order isomorphic to the primitive spectrum of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span>. Finally we show that the assignment <span><math><mi>I</mi><mo>↦</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>ℵ</mi><mo>,</mo><mi>K</mi></mrow></msub><mo>(</mo><mi>I</mi><mo>)</mo></math></span> extends to a pair of functors from <span><math><mi>P</mi><mi>o</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ℵ</mi></mrow></msub></math></span> to the category of <span><math><mi>K</mi></math></span>-algebras, one covariant and the other contravariant.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"686 ","pages":"Pages 38-100"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886414","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":"Tame fields, graded rings and finite complete sequences of key polynomials","authors":"Silva de Souza C.H.","doi":"10.1016/j.jalgebra.2025.07.046","DOIUrl":"10.1016/j.jalgebra.2025.07.046","url":null,"abstract":"<div><div>In this paper, we present a criterion for <span><math><mo>(</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> to be henselian and defectless in terms of finite complete sequences of key polynomials. For this, we use the theory of Mac Lane-Vaquié chains and abstract key polynomials. We then prove that a valued field <span><math><mo>(</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> is tame if and only if <em>vK</em> is <em>p</em>-divisible, <em>Kv</em> is perfect and every simple algebraic extension of <em>K</em> admits a finite complete sequence of key polynomials. The properties <em>vK p</em>-divisible and <em>Kv</em> perfect are described by the Frobenius endomorphism on the associated graded ring. We also make considerations on simply defectless and algebraically maximal valued fields and purely inertial and purely ramified extensions.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 550-578"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865359","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":"Twisted equivalences in spectral algebraic geometry","authors":"Chang-Yeon Chough","doi":"10.1016/j.jalgebra.2025.07.049","DOIUrl":"10.1016/j.jalgebra.2025.07.049","url":null,"abstract":"<div><div>We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks admitting a quasi-finite presentation supplies an equivalence between the stacks. Our notion thus compensates for the failure of twisted derived equivalences for non-affine schemes to provide an isomorphism of the schemes. In the case of (not necessarily connective) commutative ring spectra, we also prove a spectral analogue of Rickard's theorem, which shows that a derived equivalence of associative rings induces an isomorphism between their centers.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 474-495"},"PeriodicalIF":0.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861235","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 (k,l)-th singular locus moduli algebras of singularities and their derivation Lie algebras","authors":"Guorui Ma ,&nbsp;Stephen S.-T. Yau ,&nbsp;Huaiqing Zuo","doi":"10.1016/j.jalgebra.2025.08.007","DOIUrl":"10.1016/j.jalgebra.2025.08.007","url":null,"abstract":"<div><div>In this paper, we introduce a series of new invariants to singularities. A new conjecture about the non-existence of negative weight derivations of these new <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>)</mo></math></span>-th singular locus moduli algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture in some cases.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 673-688"},"PeriodicalIF":0.8,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865361","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":"Pushforward of Siegel flag varieties in the Chow ring","authors":"Simon Cooper","doi":"10.1016/j.jalgebra.2025.07.050","DOIUrl":"10.1016/j.jalgebra.2025.07.050","url":null,"abstract":"<div><div>Given a reductive group <em>G</em> over an algebraically closed field and subsets <span><math><mi>I</mi><mo>,</mo><mi>J</mi><mo>⊂</mo><mi>Δ</mi></math></span> of the simple roots Δ determined by a choice of maximal torus and Borel subgroup, there is a closed embedding of flag varieties <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>J</mi></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>J</mi></mrow></msub><mo>∩</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>↪</mo><mi>G</mi><mo>/</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span>. In this paper we compute the class of the sub flag variety <span><math><mo>[</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>J</mi></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>J</mi></mrow></msub><mo>∩</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>]</mo><mo>∈</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>•</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>/</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>)</mo></math></span> in the Chow ring for the ‘Siegel’ case where <em>G</em> is a general symplectic group of semisimple rank <em>g</em> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span> is the parabolic stabilising a maximal isotropic subspace. This corresponds, under the isomorphism with the tautological ring of the moduli space of principally polarised abelian varieties <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>•</mo></mrow></msup><mo>(</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mi>g</mi></mrow><mrow><mi>tor</mi></mrow></msubsup><mo>)</mo><mo>≅</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>•</mo></mrow></msup><mo>(</mo><mi>G</mi><mo>/</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>)</mo></math></span>, to the generator of the classes in the tautological ring which are supported on the toroidal boundary. This provides basic evidence for a conjecture describing the tautological ring of a Hodge-type Shimura variety.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 523-535"},"PeriodicalIF":0.8,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865358","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 structure of the character degree graphs having diameter three","authors":"Silvio Dolfi ,&nbsp;Roghayeh Hafezieh ,&nbsp;Pablo Spiga","doi":"10.1016/j.jalgebra.2025.08.002","DOIUrl":"10.1016/j.jalgebra.2025.08.002","url":null,"abstract":"<div><div>The structure of the character degree graphs <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, i.e. the prime graphs on the set <span><math><mrow><mi>cd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of the irreducible character degrees of a finite group <em>G</em>, such that <em>G</em> is solvable and <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> has diameter three, remains an intriguing area of study. However, a comprehensive understanding of these structures remains elusive. In this paper, we prove some properties and provide an infinite series of examples of this class of graphs, building on the ideas of M. Lewis <span><span>[8]</span></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 337-360"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831474","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 dual F-signature of Veronese rings","authors":"Vinicius Bouça ,&nbsp;Eliana Tolosa-Villarreal ,&nbsp;Kevin Vasconcellos","doi":"10.1016/j.jalgebra.2025.07.033","DOIUrl":"10.1016/j.jalgebra.2025.07.033","url":null,"abstract":"<div><div>In this paper we calculate explicitly the dual F-signature of the Verorese subrings of a polynomial ring in several variables, using methods of commutative algebra. This gives a positive answer to a recent conjecture proposed by Ilya Smirnov and Kevin Tucker.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 738-754"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865364","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":"Ribbon blocks for centraliser algebras of symmetric groups","authors":"Matthew Fayers ,&nbsp;Lorenzo Putignano","doi":"10.1016/j.jalgebra.2025.07.042","DOIUrl":"10.1016/j.jalgebra.2025.07.042","url":null,"abstract":"<div><div>Suppose <span><math><mi>l</mi><mo>,</mo><mi>m</mi></math></span> are natural numbers with <figure><img></figure>, and <span><math><mi>F</mi></math></span> a field of characteristic <em>p</em>, and let <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>l</mi><mo>,</mo><mi>m</mi></mrow><mrow><mi>F</mi></mrow></msubsup></math></span> denote the centraliser of the group algebra <span><math><mi>F</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> inside <span><math><mi>F</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. Ellers and Murray give a conjectured classification of the blocks of <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>l</mi><mo>,</mo><mi>m</mi></mrow><mrow><mi>F</mi></mrow></msubsup></math></span>, in terms of the <em>p</em>-blocks of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>. We prove this conjecture for a family of blocks that we call <em>ribbon blocks</em> and <em>belt blocks</em>. These are the blocks containing Specht modules labelled by skew-partitions having no repeated entries in their <em>p</em>-content.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"685 ","pages":"Pages 271-312"},"PeriodicalIF":0.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831477","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}