Related papers: Frobenius modules over multivariate Robba rings

We introduce the notion of totally reflexive extension of rings. It unifies Gorenstein orders and Frobenius extensions. We prove that for a totally reflexive extension, a module over the extension ring is totally reflexive if and only if…

Let $p$ be a prime number. There are properties called ``overconvergence'' and ``$F$-analyticity'' for $p$-adic Galois representations of a $p$-adic field $F$. By Berger's work, it is known that $F$-analyticity is stricter than…

Let $E/F$ be a quadratic extension of totally real number fields. We show that the generalized Hirzebruch-Zagier cycles arising from the associated Hilbert modular varieties can be put in $p$-adic families. As an application, using the…

This monograph is devoted to a comprehensive study of graded rings and graded K-theory. A bird's eye view of the graded module theory over a graded ring gives an impression of the module theory with the added adjective "graded" to all its…

We define the Frobenius limit of a module over a ring of prime characteristic to be the limit of the normalized Frobenius direct images in a certain Grothendieck group. When a finite group acts on a polynomial ring, we calculate this limit…

Let k be a finite field of characteristic p>0. We construct a theory of weights for overholonomic complexes of arithmetic D-modules with Frobenius structure on varieties over k. The notion of weight behave like Deligne's one in the l-adic…

We introduce the Picard group of corings. We extend the well-known exact sequence from algebras and coalgebras over fields to corings. We extend the Aut-Pic property to corings and we give some new examples of corings having this property.…

We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded…

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…

For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined…

We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.

We discuss the role of additive polynomials and $p$-polynomials in the theory of valued fields of positive characteristic and in their model theory. We outline the basic properties of rings of additive polynomials and discuss properties of…

We consider a finite acyclic quiver $\mathcal{Q}$ and a quasi-Frobenius ring $R$. We endow the category of quiver representations over $R$ with a model structure, whose homotopy category is equivalent to the stable category of…

First we study some properties of the modular group algebra $\mathbb{F}_{p^r}[G]$ where $G$ is the additive group of a Galois ring of characteristic $p^r$ and $\mathbb{F}_{p^r}$ is the field of $p^r$ elements. Secondly a description of the…

We describe the action of the different Frobenius morphisms on the cohomology ring of the moduli stack of algebraic vector bundles of fixed rank and determinant on an algebraic curve over a finite field in characteristic p and analyse…

By finite quantum groups we mean Lusztig's finite-dimensional pointed Hopf algebras called quantum Frobenius Kernels [9, 10], and their natural generalizations due to Andruskiewitsch and Schneider [2, 3]. For a Hopf algebra $H$ in a special…

We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…

In this paper, we investigate equivalent characterizations of the condition that every acyclic complex of projective, injective, or flat modules is totally acyclic over a general ring R. We provide examples to illustrate relationships among…

T. Dupuy, E. Katz, J. Rabinoff, D. Zureick-Brown introduced the module of total $p$-differentials for a ring over $Z/p^2Z$. We study the same construction for a ring over $Z_{(p)}$ and prove a regularity criterion. For a local ring, the…

We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary abelian categories. The results are strongest for module categories of rngs with enough idempotents. We also reformulate the notion of Frobenius…