相关论文: $p$-adic superspaces and Frobenius

Stark hypersurfaces are a special class of austere hypersurface in ${\mathbb C}P^n$ where the shape operator is compatible with the $CR$-structure. In this paper, the possible shape operators for stark hypersurfaces are completely…

For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of $p$-adic zeta values in the matrix entries of their $p$-adic Frobenius structure expressed in the standard basis of solutions…

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…

We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes…

We introduce and study a superversion of Dubrovin's notion of semisimple Frobenius manifolds. We establish a correspondence between semisimple Frobenius (super)manifolds and special solutions to the (supersymmetric) Schlesinger equations.…

A construction of algebraic surfaces based on two types of simple arrangements of lines, containing the prototiles of substitution tilings, has been proposed recently. The surfaces are derived with the help of polynomials obtained from…

In his foundational study of $p$-adic Hodge theory, Faltings introduced the method of almost \'etale extensions to establish fundamental comparison results of various $p$-adic cohomology theories. Scholze introduced the tilting operations…

This is an introduction to $p$-adic geometry and $p$-adic analysis focusing on the theme of $p$-adic period mappings. We follow as closely as possible the development of the classical theory of complex period mappings, blending differential…

We develop the $p$-adic representation theory of $p$-adic Lie groups on solid vector spaces over a complete non-archimedean extension of $\mathbb{Q}_p$. More precisely, we define and study categories of solid, solid locally analytic and…

The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…

We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact…

Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…

In order to have cohomological operations for de Rham p-adic cohomology with coefficients as manageable as possible, the main purpose of this paper is to solve intrinsically and from a cohomological point of view the lifting problem of…

We present a novel way of realizing the Bernoulli shift on $p$ symbols on the $p$-adic integers, where $p$ is a prime. By showing that suitably small perturbations of the shift are still Bernoulli we find many "nice" maps, such as…

We prove that $p$-adic geometric pro-\'etale cohomology of smooth partially proper rigid analytic varieties over $p$-adic fields seen in the category of Topological Vector Spaces satisfies a Poincar\'e duality as we have conjectured. This…

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with…

In this paper, we study Frobenius structures in higher dimensional $p$-adic analytic geometry and the corresponding $p$-adic functional analysis. This will build up foundations for further study on some generalized cohomology of Frobenius…

We consider a class of $q$-hypergeometric equations describing the quantum difference equation for the cotangent bundles over projective spaces $X=T^{*}\mathbb{P}^{n-1}$ . We show that over $\mathbb{Q}_p$ these equations are equipped with…

We introduce the notion of the Frobenius-Perron dimension of an integral $\Bbb Z_+$-ring and give some applications of this notion to classification of finite dimensional quasi-Hopf algebras with a unique nontrivial simple module, and of…