相关论文: Conductors and the moduli of residual perfection

Let A be a complete discrete valuation ring with possibly imperfect residue field, and let $\chi$ be a one-dimensional Galois representation over A. I show that the non-logarithmic variant of Kato's Swan conductor is the same for $\chi$ and…

For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory.

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local…

Let K be a complete discretely valued field of mixed characteristics (0, p) with perfect residue field. One of the central objects of study in p-adic Hodge theory is the category of continuous representations of the absolute Galois group of…

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was introduced recently by Faltings and appears as an equal characteristic analogue of the…

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. We first classify semi-stable representations of $G_K$ by weakly admissible filtered…

For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic…

We consider a complete discrete valuation field of characteristic p, with possibly non perfect residue field. Let V be a rank one continuous representation with finite local monodromy of its absolute Galois group. We will prove that the…

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…

For a perfect field $k$, we study actions of the absolute Galois group of $k$ on the $\bar{k}$-valued points of moduli spaces of quiver representations over $k$; the fixed locus is the set of $k$-rational points and we obtain a…

We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of…

Let $p$ be a prime, let $K$ be a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, and let $G_K$ be the Galois group. Let $\pi$ be a fixed uniformizer of $K$, let $K_\infty$ be the…

We define a motivic conductor for any presheaf with transfers $F$ using the categorical framework developed for the theory of motives with modulus by Kahn-Miyazaki-Saito-Yamazaki. If $F$ is a reciprocity sheaf this conductor yields an…

We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties…

For an ideal $I$ in a Noetherian ring $R$, we introduce and study its conductor as a tool to explore the Rees algebra of $I$. The conductor of $I$ is an ideal $C(I)\subset R$ obtained from the defining ideals of the Rees algebra and the…

We study the crystalline universal deformation ring R (and its ideal of reducibility I) of a mod p Galois representation rho_0 of dimension n whose semisimplification is the direct sum of two absolutely irreducible mutually non-isomorphic…

The perfect conductivity problem concerns optimal bounds for the magnitude of an electric field in the presence of almost touching perfect conductors. This reduces to obtaining gradient estimates for harmonic functions with Dirichlet…