Results 31 to 40 of about 12,090 (94)
Module structure of Weyl algebras
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley +1 more source
The derived category of a locally complete intersection ring [PDF]
, 2018 In this paper, we answer a question of Dwyer, Greenlees, and Iyengar by proving a local ring $R$ is a complete intersection if and only if every complex of $R$-modules with finitely generated homology is proxy small.
Pollitz, Josh
core +2 more sources
b‐Filter Grade of an Ideal a for Triangulated Categories
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let a and b be two homogeneous ideals in a graded‐commutative Noetherian ring R, and let X be an object in a compactly generated R‐linear triangulated category T. We introduce the notion of the b‐filter grade of a on X, denoted by f‐gradb,a,X, and provide several characterizations and bounds for this invariant. In addition, we explore the relationships
Li Wang +4 more
wiley +1 more source
Complete intersections and mod p cochains
, 2012 We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a space, showing ...
Avramov +13 more
core +1 more source
The shift‐homological spectrum and parametrising kernels of rank functions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird +2 more
wiley +1 more source
Counting submodules of a module over a noetherian commutative ring
, 2019 We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple module as ...
Cornulier, Yves
core +3 more sources
GL‐algebras in positive characteristic II: The polynomial ring
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley +1 more source
Classifying thick subcategories over a Koszul complex via the curved BGG correspondence
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract In this work, we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is a regular sequence and the classification of thick subcategories for an exterior algebra over a field ...
Jian Liu, Josh Pollitz
wiley +1 more source
Weakly special threefolds and nondensity of rational points
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We verify part of a conjecture of Campana predicting that rational points on the weakly special nonspecial simply connected smooth projective threefolds constructed by Bogomolov–Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps, and prove a dimension bound for such moduli spaces
Finn Bartsch +2 more
wiley +1 more source
Residually nilpotent groups of homological dimension 1
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3223-3232, October 2025.Abstract If p$p$ is a prime number, then any free group is residually a finite p$p$‐group and has homological dimension 1. As a partial converse of this assertion, in this paper we show that any finitely generated group of homological dimension 1, which is residually a finite p$p$‐group, is free.
Ioannis Emmanouil
wiley +1 more source