Related papers: Ramification filtration and differential forms

For a finite cyclic p-group G and a discrete valuation domain R of characteristic 0 with maximal ideal pR the R[G]-permutation modules are characterized in terms of the vanishing of first degree cohomology on all sub- groups (cf. Thm. A).…

Let $p$ be a prime number, $\Bbbk$ a field of characteristic $p$ and $G$ a finite $p$-group acting on a standard graded polynomial ring $S = \Bbbk[x_1, \ldots, x_n]$ as degree-preserving $\Bbbk$-algebra automorphisms. Assume that $G$ is…

Let $k$ be a field of characteristic $p$, let $P$ be a finite $p$- group, where $p$ is an odd prime, and let $D(P)$ be the Dade group of endo-permutation $kP$-modules. It is known that $D(P)$ is detected via deflation--restriction by the…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

For a Henselian discrete valued field $K$ of characteristic $p>0$, Kato defined a ramification filtration $\{{\rm fil}_nH^q(K,\mathbb Q_p/\mathbb Z_p(q-1))\}_{n \ge 0}$ on $H^q(K,\mathbb Q_p/\mathbb Z_p(q-1))$. One can also define a…

Let $p$ be a prime number, $n>2$ an integer, and $F$ a CM field in which $p$ splits completely. Assume that a continuous automorphic Galois representation…

Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

This article is devoted to studying the ramification of Galois torsors and of $\ell$-adic sheaves in characteristic $p>0$ (with $\ell\not=p$). Let $k$ be a perfect field of characteristic $p>0$, $X$ be a smooth, separated and quasi-compact…

For a local field with finite residue field of characteristique p, we give some refinements of Serre's mass formula in degree p which allow us to compute for example the contribution of cyclic extensions, or of those whose galoisian closure…

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in…

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 $G_k$…

We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

Ramification invariants are necessary, but not in general sufficient, to determine the Galois module structure of ideals in local number field extensions. This insufficiency is associated with elementary abelian extensions, where one can…

In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded…

We establish a "matrix simultaneous diagonalization theorem" for disconnected reductive groups which relaxes both the semisimplicity condition and the commutativity condition. As an application, we prove the following basic results…

Suppose G is a semi-direct product of the form Z/p^n \rtimes Z/m where p is prime and m is relatively prime to p. Suppose K is a local field of characteristic p > 0. The main result states necessary and sufficient conditions on the…

We give a construction of a large first-order definable family of subrings of finitely generated fields $K$ of any characteristic. We deduce that for any such $K$ there exists a first-order sentence $\varphi_K$ characterising $K$ in the…

In this article, we describe the structure of the $R$-algebra of Drinfeld modular forms $M(\Gamma_0(T))_R$ (resp., $M^0(\Gamma_0(T))_R$) of level $\Gamma_0(T)$ and the structure of mod-$\p$ reduction of $M_{\mfp}^0(\Gamma_0(T))$ for $\p…