Related papers: A comparison between compactly supported rigid and…
We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant…
We lay the groundwork for a Riemann-Hilbert correspondence for Ardakov-Wadsley's D-cap-modules by introducing corresponding solution and de Rham functors. Our constructions rely on Scholze's $p$-adic Hodge theory for rigid-analytic…
This paper endeavors to explore certain distinguished modules and subcategories within mod$\Lambda$. Let $\mathrm{proj}\mbox{-}\Lambda$ denote the category of all finitely generated projective $\Lambda$-modules and define…
The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations…
We construct \Lambda-adic de Rham and crystalline analogues of Hida's ordinary \Lambda-adic etale cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of \Q_p, we prove appropriate…
Let $k$ be a perfect field of characteristic $p>0$, $\mathcal{V}$ a complete discrete valuation ring with residue field $k$ and field of fractions $K$ of characteristic 0, and $S$ a separated $k$-scheme of finite type. When $S$ is smooth…
We show that the arithmetic D-module associated to an overconvergent F-isocrystal over a smooth curve is holonomic. We first prove that unipotent F-isocrystals are holonomic D-module by using the fact that such F-isocrystals come from…
We define and study the Hochschild (co)homology of the second kind (known also as the Borel-Moore Hochschild homology and the compactly supported Hochschild cohomology) for curved DG-categories. An isomorphism between the Hochschild…
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated…
Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…
We study holonomic D-modules on SL_n(C)xC^n, called mirabolic modules, analogous to Lusztig's character sheaves. We describe the supports of simple mirabolic modules. We show that a mirabolic module is killed by the functor of Hamiltonian…
We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…
We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld's refinement of the…
A. D'Agnolo and M. Kashiwara proved that their enhanced solution functor induces a fully faithful embedding of the triangulated category of holonomic D-modules into the one of R-constructible enhanced ind-sheaves. In this paper, we define…
After works by Katz, Monsky, and Adolphson-Sperber, a comparison theorem between relative de Rham cohomology and Dwork cohomology is established in a paper by Dimca-Maaref-Sabbah-Saito in the framework of algebraic D-modules. We propose…
In this article, we will explore the fundamental concepts, including various basic concepts on $d$-complex manifolds, along with several differential operators and examine the relationships between them. A $d$-K\"ahler manifold is a…
This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the…
Given a liftable smooth proper variety over $\mathbb{F}_p$, we construct the moduli stacks of crystals and isocrystals on it. We show that the former is a formal algebraic stack over $\mathbb{Z}_p$ and the latter is an adic stack -- Artin…
We construct in an abstract fashion the orbifold quantum cohomology (quantum orbifold cohomology) of weighted projective space, starting from the orbifold quantum differential operator. We obtain the product, grading, and intersection form…
We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined contramodules'' over a triple $(\mathscr C,A,\psi)$, where…