Related papers: Two interesting examples of $\mathcal{D}$-modules …

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

We consider irreducible lowest-weight representations of Cherednik algebras associated to certain classes of complex reflection groups in characteristic p. In particular, we study maximal graded submodules of Verma modules associated to…

We investigate the Lyubeznik numbers, and the injective dimension of local cohomology modules, of finitely generated $\mathbb{Z}$-algebras. We prove that the mixed characteristic Lyubeznik numbers and the standard ones agree locally for…

We prove a formula for special L-values of Anderson's modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.

This work is motivated by the papers [EG85] and [Ngu15] in which the following two problems are solved. Let $\mathcal{O}$ is a finitely generated $\mathbb{Z}$-algebra that is an integrally closed domain of characteristic zero, consider the…

In this paper we study a correspondence between cyclic modules over the first Weyl algebra and planar algebraic curves in positive characteristic. In particular, we show that any such curve has a preimage under a morphism of certain…

We observe that the characteristic cycle of a D-module gives bounds for decomposition numbers of intersection cohomology complexes.

In this article we fix a prime integer $p$ and compare certain dg algebra resolutions over a local ring whose residue field has characteristic $p$. Namely, we show that given a closed surjective map between such algebras there is a precise…

We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers $p$. We offer an elementary approach based on a counting method. The outcome is a weak form of the Lang-Weil lower bound…

We study the $p$-rank stratification of the moduli space $\mathcal{ASW}_{(d_1,d_2,\ldots,d_n)}$, which represents $\mathbb{Z}/p^n$-covers in characteristic $p>0$ whose $\mathbb{Z}/p^i$-subcovers have conductor $d_i$. In particular, we…

Let $\bbk$ be an algebraically closed field of prime characteristic $p$. If $p$ does not divide $n$, irreducible modules over $\frak {sl}_n$ for regular and subregular nilpotent representations have already known(see \cite{Jan2} and…

We study Poisson traces of the structure algebra A of an affine Poisson variety X defined over a field of characteristic p. According to arXiv:0908.3868v4, the dual space HP_0(A) to the space of Poisson traces arises as the space of…

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a…

It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the…

We develop the theory of adequate moduli spaces in characteristic $p$ (and mixed characteristic) characterizing quotients by geometrically reductive group schemes.

In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…

We construct polynomial solutions modulo $p^s$ of the differential KZ and dynamical equations where $p$ is an odd prime number.

We give an alternative proof to the annihilator of local cohomology in characteristic zero which was proved by Lyubeznik.

Let $k$ be a field of positive characteristic $p>2$. We prove a duality property concerning the kernel of coinduced representations of Lie superalgebras. This property was already proved by M. Duflo for Lie algebras in any characteristic…

We give an overview of the theory of $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces and its applications to admissible locally analytic representations of $p$-adic Lie groups.