Related papers: A $p$-Adic 6-Functor Formalism in Rigid-Analytic G…

This paper introduces an abelian category of logarithmic coherent sheaves that arranges coherent sheaves across all expansions and root stacks of a simple normal crossing degeneration. Formally, logarithmic coherent sheaves are coherent…

We introduce all six operations for D-cap-modules on smooth rigid analytic spaces by considering the derived category of complete bornological D-cap-modules. We then focus on a full subcategory which should be thought of as consisting of…

Whatever it is that animates anima and breathes life into higher algebra, this something leaves its trace in the structure of a Dirac ring on the homotopy groups of a commutative algebra in spectra. In the prequel to this paper, we…

In this article, we develop a theory of Grothendieck's six operations for derived categories in \'etale cohomology of Artin stacks, for both torsion and adic coefficients. We prove several desired properties of the operations, including the…

In this note we realize the sheaf of Cherednik algebras $H_{1, c, X, G}$ on a general good complex orbifold $X/G$, originally introduced by Etingof for smooth complex varieties with an action by a finite group, by gluing sheaves of flat…

We prove that algebraic de Rham cohomology as a functor defined on smooth $\mathbb{F}_p$-algebras is formally \'etale in a precise sense. This result shows that given de Rham cohomology, one automatically obtains the theory of crystalline…

We present an analytic approximation model for non-rigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured…

Deninger and Werner developed an analogue for p-adic curves of the classical correspondence of Narasimhan and Seshadri between stable bundles of degree zero and unitary representations of the topological fundamental group for a complex…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

We define analytic torsion for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold X valued in a flat vector bundle E, with a differential given by a flat connection on E…

We begin the systematic study of cohomological Hecke operators of modifications of coherent sheaves on a smooth surface $X$, along a fixed proper curve $Z \subset X$. We develop the necessary geometric foundations in order to define the…

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…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…

We investigate deformations of the shuffl e Hopf algebra structure Sh(A) which can be de fined on the tensor algebra over a commutative algebra A. Such deformations, leading for example to the quasi-shuffl e algebra QSh(A), can be…

In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for \'etale cohomology of Artin stacks and prove several desired properties including the base change theorem. In addition, we define perverse t-structures…

In order to study $p$-adic \'etale cohomology of an open subvariety $U$ of a smooth proper variety $X$ over a perfect field of characteristic $p>0$, we introduce new $p$-primary torsion sheaves. It is a modification of the logarithmic de…

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…

Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $\overline{\mathbb F}_\ell$-sheaves. The universal deformation…

We construct a canonical sesquilinear pairing on the relative crystalline cohomology of a smooth proper family of varieties over a complete discretely valued $p$-adic field. Motivated by the role of Saito's higher residue pairing in the…