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Archiv der Mathematik最新文献

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Mixed multiquadratic splitting fields 混合多二次分裂场
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-14 DOI: 10.1007/s00013-025-02135-9
Fatma Kader Bingöl, Adam Chapman, Ahmed Laghribi
{"title":"Mixed multiquadratic splitting fields","authors":"Fatma Kader Bingöl,&nbsp;Adam Chapman,&nbsp;Ahmed Laghribi","doi":"10.1007/s00013-025-02135-9","DOIUrl":"10.1007/s00013-025-02135-9","url":null,"abstract":"<div><p>We study mixed multiquadratic field extensions as splitting fields for central simple algebras of exponent 2 in characteristic 2. As an application, we provide examples of nonexcellent mixed biquadratic field extensions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"29 - 37"},"PeriodicalIF":0.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02135-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On maximally symmetric subalgebras 关于极大对称子代数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-14 DOI: 10.1007/s00013-025-02132-y
Alexander Kleshchev
{"title":"On maximally symmetric subalgebras","authors":"Alexander Kleshchev","doi":"10.1007/s00013-025-02132-y","DOIUrl":"10.1007/s00013-025-02132-y","url":null,"abstract":"<div><p>Let <span>(mathbb {k})</span> be a characteristic zero Dedekind domain, <i>S</i> be a <span>(mathbb {k})</span>-algebra, and <span>(Tsubseteq S)</span> be a full rank subalgebra. Suppose the algebra <i>T</i> is symmetric. It is important to know when <i>T</i> is a <i>maximally symmetric subalgebra</i> of <i>S</i>, i.e., no <span>(mathbb {k})</span>-subalgebra <i>C</i> satisfying <span>(Tsubsetneq Csubseteq S)</span> is symmetric. In this note, we establish a useful sufficient condition for this using a notion of a quasi-unit of an algebra. This condition is used to obtain an old and a new result on maximal symmetricity for generalized Schur algebras corresponding to certain Brauer tree algebras. The old result was used in our work with Evseev on RoCK blocks of symmetric groups. The new result will be used in our forthcoming work on RoCK blocks of double covers of symmetric groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"123 - 132"},"PeriodicalIF":0.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02132-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Resolutions over strict complete intersections 在严格的完整交叉点上的分辨率
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-14 DOI: 10.1007/s00013-025-02133-x
Tony J. Puthenpurakal
{"title":"Resolutions over strict complete intersections","authors":"Tony J. Puthenpurakal","doi":"10.1007/s00013-025-02133-x","DOIUrl":"10.1007/s00013-025-02133-x","url":null,"abstract":"<div><p>Let <span>((Q, mathfrak {n} ))</span> be a regular local ring and let <span>(f_1, ldots , f_c in mathfrak {n} ^2)</span> be a <i>Q</i>-regular sequence. Set <span>((A, mathfrak {m} ) = (Q/(textbf{f} ), mathfrak {n} /(textbf{f} )))</span>. Further assume that the initial forms <span>(f_1^*, ldots , f_c^*)</span> form a <span>(G(Q) = bigoplus _{n ge 0}mathfrak {n} ^i/mathfrak {n} ^{i+1})</span>-regular sequence. Without loss of any generality, assume <span>(operatorname {ord}_Q(f_1) ge operatorname {ord}_Q(f_2) ge cdots ge operatorname {ord}_Q(f_c))</span>. Let <i>M</i> be a finitely generated <i>A</i>-module and let <span>((mathbb {F} , partial ))</span> be a minimal free resolution of <i>M</i>. Then we prove that <span>(operatorname {ord}(partial _i) le operatorname {ord}_Q(f_1) - 1)</span> for all <span>(i gg 0)</span>. We also construct an MCM <i>A</i>-module <i>M</i> such that <span>(operatorname {ord}(partial _{2i+1}) = operatorname {ord}_Q(f_1) - 1)</span> for all <span>(i ge 0)</span>. We also give a considerably simpler proof regarding the periodicity of ideals of minors of maps in a minimal free resolution of modules over arbitrary complete intersection rings (not necessarily strict).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"17 - 28"},"PeriodicalIF":0.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 maximality of T in Thompson’s group V 汤普森组V中T的最大值
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-14 DOI: 10.1007/s00013-025-02136-8
J. Belk, C. Bleak, M. Quick, R. Skipper
{"title":"The maximality of T in Thompson’s group V","authors":"J. Belk,&nbsp;C. Bleak,&nbsp;M. Quick,&nbsp;R. Skipper","doi":"10.1007/s00013-025-02136-8","DOIUrl":"10.1007/s00013-025-02136-8","url":null,"abstract":"<div><p>We show that R. Thompson’s group <i>T</i> is a maximal subgroup of the group <i>V</i>. The argument provides examples of foundational calculations which arise when expressing elements of <i>V</i> as products of transpositions of basic clopen sets in the Cantor space <span>(mathfrak {C})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"1 - 7"},"PeriodicalIF":0.5,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02136-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A weighted weak-type multilinear gradient inequality 一个加权弱型多线性梯度不等式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-07 DOI: 10.1007/s00013-025-02124-y
Víctor García García, Pedro Ortega Salvador
{"title":"A weighted weak-type multilinear gradient inequality","authors":"Víctor García García,&nbsp;Pedro Ortega Salvador","doi":"10.1007/s00013-025-02124-y","DOIUrl":"10.1007/s00013-025-02124-y","url":null,"abstract":"<div><p>We characterize the weights <span>(w, v_1, v_2, dots , v_m )</span> for which the weak-type multilinear gradient inequality </p><div><div><span>$$begin{aligned} left| prod _{i=1}^m f_iright| _{p,infty ;w}le C prod _{i=1}^m left| x cdot nabla f_i(x)right| _{p_i,v_i} end{aligned}$$</span></div></div><p>holds for all <span>(f_1, f_2, dots , f_m in C_c^{infty }({mathbb {R}}^n))</span> in the case <span>(frac{1}{p} = frac{1}{p_1}+frac{1}{p_2}+ cdots + frac{1}{p_m})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"683 - 693"},"PeriodicalIF":0.5,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02124-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decomposition of Jacobians and Shimura subvarieties of (A_g) 的雅可比矩阵和Shimura子变种的分解 (A_g)
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-07 DOI: 10.1007/s00013-025-02123-z
Abolfazl Mohajer
{"title":"Decomposition of Jacobians and Shimura subvarieties of (A_g)","authors":"Abolfazl Mohajer","doi":"10.1007/s00013-025-02123-z","DOIUrl":"10.1007/s00013-025-02123-z","url":null,"abstract":"<div><p>Using the decomposition of Jacobians with group action, we prove the non-existence of some Shimura subvarieties in the moduli space of ppav <span>(A_{g})</span> arising from families of dihedral and quaternionic covers of the complex projective line <span>({{mathbb {P}}}^1)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"53 - 61"},"PeriodicalIF":0.5,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02123-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit computation of the field of moduli of some non-hyperelliptic pseudo-real curves 一类非超椭圆伪实曲线模场的显式计算
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-07 DOI: 10.1007/s00013-025-02130-0
Rubén A. Hidalgo
{"title":"Explicit computation of the field of moduli of some non-hyperelliptic pseudo-real curves","authors":"Rubén A. Hidalgo","doi":"10.1007/s00013-025-02130-0","DOIUrl":"10.1007/s00013-025-02130-0","url":null,"abstract":"<div><p>For each even integer <span>(k ge 2)</span>, we construct an explicit real two-dimensional family <span>(C^{(k)}_{r,theta })</span> of non-hyperelliptic pseudo-real Riemann surfaces of genus <span>(g=1+(2k-3)k^{4})</span>. For each of them, we compute its field of moduli and also a minimal field of definition.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 1","pages":"63 - 77"},"PeriodicalIF":0.5,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 lattice illumination of smooth convex bodies 光滑凸体的点阵光照
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-05-01 DOI: 10.1007/s00013-025-02128-8
Lenny Fukshansky
{"title":"On lattice illumination of smooth convex bodies","authors":"Lenny Fukshansky","doi":"10.1007/s00013-025-02128-8","DOIUrl":"10.1007/s00013-025-02128-8","url":null,"abstract":"<div><p>The illumination conjecture is a classical open problem in convex and discrete geometry, asserting that every compact convex body <i>K</i> in <span>(mathbb {R}^n)</span> can be illuminated by a set of no more than <span>(2^n)</span> points. If <i>K</i> has smooth boundary, it is known that <span>(n+1)</span> points are necessary and sufficient. We consider an effective variant of the illumination problem for bodies with smooth boundary, where the illuminating set is restricted to points of a lattice and prove the existence of such a set close to <i>K</i> with an explicit bound on the maximal distance. We produce improved bounds on this distance for certain classes of lattices, exhibiting additional symmetry or near-orthogonality properties. Our approach is based on the geometry of numbers.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"133 - 143"},"PeriodicalIF":0.5,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145141855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Rice theorem for dynamical properties of SFTs on groups 群上SFTs动力学性质的一个Rice定理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-29 DOI: 10.1007/s00013-025-02125-x
Nicanor Carrasco-Vargas
{"title":"On a Rice theorem for dynamical properties of SFTs on groups","authors":"Nicanor Carrasco-Vargas","doi":"10.1007/s00013-025-02125-x","DOIUrl":"10.1007/s00013-025-02125-x","url":null,"abstract":"<div><p>Let <i>G</i> be a group with undecidable domino problem, such as <span>({mathbb {Z}}^2)</span>. We prove that all nontrivial dynamical properties for sofic <i>G</i>-subshifts are undecidable, that this is not true for <i>G</i>-SFTs, and an undecidability result for dynamical properties of <i>G</i>-SFTs similar to the Adian–Rabin theorem. Furthermore, we prove that every computable real-valued dynamical invariant for <i>G</i>-SFTs that is monotone by disjoint unions and products is constant.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"124 6","pages":"591 - 603"},"PeriodicalIF":0.5,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Brill-Noether loci on an Enriques surface covered by a Jacobian Kummer surface 由Jacobian Kummer曲面覆盖的Enriques曲面上的Brill-Noether轨迹
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-04-29 DOI: 10.1007/s00013-025-02129-7
I. Macías Tarrío, C. Spiridon, A. Stoenicǎ
{"title":"Brill-Noether loci on an Enriques surface covered by a Jacobian Kummer surface","authors":"I. Macías Tarrío,&nbsp;C. Spiridon,&nbsp;A. Stoenicǎ","doi":"10.1007/s00013-025-02129-7","DOIUrl":"10.1007/s00013-025-02129-7","url":null,"abstract":"<div><p>The aim of this note is to exhibit proper first Brill-Noether loci inside the moduli spaces <span>(M_{Y,H}(2;c_1,c_2))</span> of <i>H</i>-stable rank 2 vector bundles with fixed Chern classes of a certain type on an Enriques surface <i>Y</i> which is covered by a Jacobian Kummer surface <i>X</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 2","pages":"145 - 156"},"PeriodicalIF":0.5,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02129-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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