相关论文: Swan conductors for p-adic differential modules, I…

Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an isocrystal on a variety over a perfect field of positive characteristic overconvergent along a boundary divisor;…

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 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…

Let k be a complete discrete valuation field of equal characteristic p>0. Using the tools of p-adic differential modules, we define refined Artin and Swan conductors for a representation of the absolute Galois group $G_k$ with finite local…

Let $k$ be a complete discretely valued field of equal characteristic $p > 0$ with possibly imperfect residue field and let $G_k$ be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on $G_k$…

There are two ways to define the Swan conductor of an abelian character of the absolute Galois group of a complete discrete valuation field. We prove that these two Swan conductors coincide.

Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on Br X. We relate this filtration to that defined by Kato's Swan conductor. The refined…

The refined Swan conductor is defined by K.\ Kato \cite{KK2}, and generalized by T.\ Saito \cite{wild}. In this part, we consider some smooth $l$-adic \'{e}tale sheaves of rank $p$ such that we can be define the $rsw$ following T.\ Saito,…

We prove the formal degree conjecture for simple supercuspidal representations of symplectic groups and quasi-split even special orthogonal groups over a p-adic field, under the assumption that p is odd. The essential part is to compute the…

We consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic zero. This extends prior…

We construct the local Galois representations over the complex field whose Swan conductors are one by using etale cohomology of Artin-Schreier sheaves on affine lines over finite fields. Then, we study the Galois representations, and give…

Let $C=A(r, r')$ be a closed annulus of radii $r$ and $r'$ ($r < r' \in \mathbb{Q}_{\geq 0}$) over a complete discrete valuation field with algebraically closed residue field of characteristic $p>0$. To an \'etale sheaf of…

This article studies the variation of the Swan conductor of a lisse \'etale sheaf of $\mathbb{F}_{\ell}$-modules $\mathcal{F}$ on the rigid unit disc $D$ over a complete discrete valuation field $K$ with algebraically closed residue field…

Let A be a complete discrete valuation ring with possibly imperfect residue field. The purpose of this paper is to give a notion of conductor for Galois representations over A that generalizes the classical Artin conductor. The definition…

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…

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification…

Let $F$ be a local non-Archimedean field and $E$ a finite Galois extension of $F$, with Galois group $G$. If $\rho$ is a representation of $G$ on a complex vector space $V$, we may compose it with any tensor operation $R$ on $V$, and get…

The Grothendieck-Ogg-Shafarevich formula calculates the l-adic Euler-Poincare number of an l-adic sheaf on a curve by an invariant produced by the wild ramification of the l-adic sheaf named Swan class. A. Abbes, K. Kato and T. Saito…

Let $K$ be a complete discrete valuation field of mixed characteristic $(0,p)$, whose residue field may not be perfect, and $G_K$ the absolute Galois group of $K$. In the first part of this paper, we prove that Scholl's generalization of…

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…