Results 31 to 40 of about 121 (115)
On The Cohomological Dimension of Local Cohomology Modules
, 2015 Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module with $\operatorname{cd}(I,M)=c$. In this article, we first show that there exists a descending chain of ideals $I=I_c\supsetneq I_{c-1}\supsetneq \cdots \supsetneq I_0$ of $R$ such that for each $0\leq i\leq c-1$, $\operatorname{cd}(I_i,M)=i$ and that the top local cohomology ...
Erdoǧdu, Vahap, Yıldırım, Tuǧba
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The mod 2 Seiberg–Witten invariants of spin structures and spin families
Journal of Topology, Volume 19, Issue 4, December 2026.Abstract We completely determine the mod 2 Seiberg–Witten invariants for any spin structure on any closed, oriented, smooth 4‐manifold X$X$. Our computation confirms the validity of the simple‐type conjecture mod 2 for spin structures. Our proof also works for families of spin 4‐manifolds and thus computes the mod 2 Seiberg–Witten invariants for spin ...
David Baraglia
wiley +1 more source
Graded Components of Local Cohomology Modules II
Vietnam Journal of Mathematics, 2022 Section 10 has been ...
Puthenpurakal, Tony J., Roy, Sudeshna
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Non‐Geometric T‐Duality as Higher Groupoid Bundles With Connections
Fortschritte der Physik, Volume 74, Issue 10, October 2026.This paper describes T‐duality between geometric and non‐geometric backgrounds using spans of higher groupoid bundles with adjusted connections. This framework incorporates explicit metric formulas, scalar fields, and Q$Q$‐fluxes. The resulting model reproduces key literature examples while maintaining covariance under the full T‐duality group O(n,n;Z)$
Hyungrok Kim, Christian Saemann
wiley +1 more source
On the maximum likelihood degree of Gaussian graphical models
Bulletin of the London Mathematical Society, Volume 58, Issue 10, October 2026.Abstract In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML‐degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML‐degree of the nth$n{\rm th}$ cycle is larger than 1 for any n⩾4$n\geqslant 4$, therefore completing the characterization ...
Carlos Améndola +3 more
wiley +1 more source
$D$-module and $F$-module length of local cohomology modules [PDF]
Transactions of the American Mathematical Society, 2018 Let $R$ be a polynomial or power series ring over a field $k$. We study the length of local cohomology modules $H^j_I(R)$ in the category of $D$-modules and $F$-modules. We show that the $D$-module length of $H^j_I(R)$ is bounded by a polynomial in the degree of the generators of $I$.
Katzman, M. +3 more
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bk$b^k$‐Algebroids and the variety of foliation jets
Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.Abstract We introduce and classify singular foliations of bk+1$b^{k+1}$‐type, which formalize the properties of vector fields that are tangent to a submanifold W⊂M$W \subset M$ to order k$k$. When W$W$ is a hypersurface, these structures are Lie algebroids generalizing the bk+1$b^{k+1}$‐tangent bundles introduced by Scott.
Francis Bischoff +2 more
wiley +1 more source
Artinianness of formal local cohomology modules [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2019 Summary: Let \(\mathfrak{a}\) be an ideal of Noetherian local ring \((R,\mathfrak{m})\) and \(M\) a finitely generated \(R\)-module of dimension \(d\). In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to \(\mathfrak{m}\).
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Abelian number fields with frobenian conditions
Mathematika, Volume 72, Issue 4, October 2026.Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
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Matlis duals of top Local cohomology modules [PDF]
Proceedings of the American Mathematical Society, 2007 In the first section of this paper we present generalizations of known results on the set of associated primes of Matlis duals of local cohomology modules; we prove these generalizations by using a new technique. In section 2 we compute the set of associated primes of the Matlis dual of
Hellus, Michael, Stückrad, Jürgen
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