相关论文: Lagrangianity for log extendable overconvergent $F…

In this paper, we prove the generic overconvergence of relative rigid cohomology with coefficient, by using the semistable reduction conjecture for overconvergent $F$-isocrystals (which is recently shown by Kedlaya).

In this paper we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for…

We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open…

Let $X_0$ be a smooth geometrically connected variety defined over a finite field $\mathbb F_q$ and let $\mathcal E_0^{\dagger}$ be an irreducible overconvergent $F$-isocrystal on $X_0$. We show that if a subobject of minimal slope of the…

Let $G$ be a simple simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$, with $r$-th Frobenius kernel $G_r$. Let $M$ be a $G_r$-module and $V$ a rational $G$-module. We put a variety structure on…

Inspired by a theorem of Bhatt-Morrow-Scholze, we develop a stacky approach to crystals and isocrystals on "Frobenius-smooth" schemes over F_p . This class of schemes goes back to Berthelot-Messing and contains all smooth schemes over…

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent…

Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the…

The aim of the present paper is to study arithmetic properties of $\mathcal{D}$-modules on an algebraic variety over the field of algebraic numbers. We first provide a framework for extending a class of $G$-connections (resp., globally…

We describe mirror symmetry for weak toric Fano manifolds as an equivalence of D-modules equipped with certain filtrations. We discuss in particular the logarithmic degeneration behavior at the large radius limit point, and express the…

Let $X$ be a smooth scheme over a finite field. It is conjectured that a convergent $F$-isocrystal on $X$ is overconvergent if its restriction to every curve contained in $X$ is overconvergent. Using the theory of \'etale and crystalline…

Let $\V$ be a mixed characteristic complete discrete valuation ring with perfect residue field $k$. We solve Berthelot's conjectures on the stability of the holonomicity over smooth projective formal $\V$-schemes. Then we build a category…

For varieties over a perfect field of characteristic p, etale cohomology with Q_l-coefficients is a Weil cohomology theory only when l is not equal to p; the corresponding role for l = p is played by Berthelot's rigid cohomology. In that…

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…

In this note we sketch a proof of a fundamental conjecture, the codimension-three conjecture, for microdifferential holonomic systems with regular singularities. It states that any regular holonomic E-module extends beyond a…

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly…

We show that unit $\mathcal{O}_{F,X}^\Lambda$-modules of Emerton and Kisin provide an analogue of locally constant sheaves in the context of B\"ockle-Pink $\Lambda$-crystals. For example they form a tannakian category if the coefficient…

We study the category of holonomic $\mathscr{D}_{X}$-modules for a quasi-compact, quasi-separated, smooth rigid analytic variety $X$ over the field $\mathbb{C}(\!(t)\!)$. In particular, we prove finiteness of the de Rham cohomology for such…