Related papers: Some properties and applications of $F$-finite $F$…
Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated…
We develop a formalism of unit $F$-modules in the style of Lyubeznik and Emerton-Kisin for rings which have finite $F$-representation type after localization and completion at every prime ideal. As applications, we show that if $R$ is such…
We search for some splitting (resp. finiteness) criteria of a given module $M$ over a local ring $(R,\fm,k)$ in terms of the splitting (resp. finiteness) property of certain cohomological functors evaluated at $M$. In particular, we deal…
Let G be a simply connected semisimple algebraic group over an algebraically closed field k of positive characteristic. We will untwist the structure of G-modules by a newly found splitting of the Frobenius endomorphism on the algebra of…
Smith and Van den Bergh introduced the notion of finite F-representation type as a characteristic $p$ analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite…
It is well known that if G is a finite group then the group of endotrivial modules is finitely generated. In this paper we investigate endotrivial modules over arbitrary finite group schemes. Our results can be applied to computing the…
This paper builds on work of Hochster and Yao that provides nice embeddings for finitely generated modules of finite G-dimension, finite projective dimension, or locally finite injective dimension. We extend these results by providing…
We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the $\mathbb{F}_q$-isomorphism classes…
A flat-injective presentation of a multiparameter persistence module $M$ characterizes $M$ as the image of a morphism from a flat to an injective persistence module. Like flat or injective presentations, flat-injective presentations can be…
The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with seminegative curvature on a compact Kaehler manifold. There are in fact…
We present an algorithm for computing the structure of any submodule of the module of points of a Drinfeld $A$-module over a finite field, where $A$ is a function ring over $\mathbb F_q$. When the function ring is $A = \mathbb F_q[T]$, we…
Let $R$ be a commutative Noetherian local ring of prime characteristic $p$ and $f:R\to R$ the Frobenius ring homomorphism. For $e\ge 1$ let $R^{(e)}$ denote the ring $R$ viewed as an $R$-module via $f^e$. Results of Peskine, Szpiro, and…
The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these…
In this paper we present a condition on a local Cohen-Macaulay F-injective ring of positive characteristic $p > 2$ which implies that its top local cohomology module with support in the maximal ideal has finitely many Frobenius compatible…
Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…
We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein) projective dimension with respect to a semidualizing module. We also verify special cases of a question of…
The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…
Motivated by the problem of determining the structure of integral points on subvarieties of semiabelian varieties defined over finite fields, we prove a quantifier elimination result for certain modules over finite simple extensions of the…
We use a result of Hellus about generalized local duality to describe some generalized Matlis duals for certain quasi-\F-modules. Furthermore, we apply this description to obtain examples for non-artinian local cohomology modules by the…
We introduce a type of graph integrals which are holomorphic analogs of configuration space integrals. We prove their (ultraviolet) finiteness by considering a compactification of the moduli space of graphs with metrics, and study their…