Finite F-representation type is an important notion in characteristic p commutative algebra,
but explicit examples of varieties with or without this property are few. We prove that a large …

In this article, we show that the Frobenius test exponent for parameter ideals of a local ring of
prime characteristic is always bigger than or equal to its Hartshorne–Speiser–Lyubeznik …

Let $ R=\bigoplus_ {i\geq 0} R_i $ be a Noetherian commutative non-negatively graded ring
such that $(R_0,\mathfrak {m} _0) $ is a Henselian local ring. Let $\mathfrak {m} $ be its …

This manuscript discusses many problems connected with finiteness properties of local
cohomology modules, eg the associated primes, the minimal primes, Bass numbers, as well …

In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-
modules for rings of invariants of finite groups in characteristic zero, and for strongly F …

We study the question of when a ring can be realized as a direct summand of a regular ring
by examining the case of homogeneous coordinate rings. We present very strong obstacles …

Let $(R,\frak {m}) $ be a local ring and $ I, J $ two arbitrary ideals of $ R $. Let $ gr_J (R/I) $
denote the associated graded ring of $ R/I $ with respect to $ J $, which corresponds to the …

Let $ V $ be a finite rank vector space over a perfect field of characteristic $ p> 0$, and let $
G $ be a finite subgroup of $\operatorname {GL}(V) $. If $ V $ is a permutation …

We develop a formalism of unit-modules in the style of Lyubeznik and Emerton-Kisin for
rings that have finite-representation type after localization and completion at every prime …

In this manuscript, we prove the Bernstein inequality and develop the theory of holonomic-
modules for rings of invariants of finite groups in characteristic zero, and for strongly-regular …