Related papers: Lifting the field of norms

Let $K$ be a finite extension of $\mathbf{Q}_p$. The field of norms of a strictly APF extension $K_\infty/K$ is a local field of characteristic $p$ equipped with an action of $\mathrm{Gal}(K_\infty/K)$. When can we lift this action to…

Fix $K/\mathbf{Q}_p$ a finite extension and let $L/K$ be an infinite, strictly APF extension in the sense of Fontaine--Wintenberger. Let $X_K(L)$ denote its associated norm field. The goal of this paper is to associate to $L/K$, in a…

We prove that every place of an algebraic function field F|K of arbitrary characteristic admits local uniformization in a finite extension F' of F. We show that F'|F can be chosen to be normal. If K is perfect and P is of rank 1, then…

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible…

Let $k$ be a finite field. Wintenberger used the field of norms to give an equivalence between a category whose objects are totally ramified abelian $p$-adic Lie extensions $E/F$, where $F$ is a local field with residue field $k$, and a…

We consider an infinite extension $K$ of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. $K$ is equipped with an inductive limit topology; its conjugate $\bar{K}$ is a completion of $K$…

We study divided power structures on finitely generated $k$-algebras, where $k$ is a field of positive characteristic $p$. As an application we show examples of $0$-dimensional Gorenstein $k$-schemes that do not lift to a fixed noetherian…

We describe integral lifts K(L), indexed by local fields L of degree n = [L:\Q_p], of the extraordinary cohomology theories K(n), and apply the generalized character theory of Hopkins, Kuhn and Ravenel to identify K(L)(BG) \otimes \Q$, for…

Suppose that $\pi \: Y \to X$ is a finite map of normal varieties over a perfect field of characteristic $p > 0$. Previous work of the authors gave a criterion for when Frobenius splittings on $X$ (or more generally any $p^{-e}$-linear map)…

Let $G=D_p$ be the dihedral group of order $2p$, where $p$ is an odd prime. Let $k$ an algebraically closed field of characteristic $p$. We show that any action of $G$ on the ring $k[[y]]$ can be lifted to an action on $R[[y]]$, where $R$…

Let $K$ be a field complete with respect to a nonarchimedean real-valued norm, and let $L/K$ be an algebraic extension. We show that there is a unique norm on $L$ extending the given norm on $K$, with an explicit description. As an…

In this paper, the author proved that the base change lifting associated to a totally ramified extension of a non-archimedean local field coincides with a map coming from the close fields theory of Kazhdan under some conditions. As a…

Let $k$ be an algebraically closed field of characteristic $2$. In this paper we describe the $(\mathbb{Z}/2\mathbb{Z})^3$-actions on $k[[z]]$ for which there is a discrete valuation ring $R$, a finite extension of the ring of Witt vectors…

The main aim of this article is to give new classes of smooth projective varieties over characteristic $p>0$ that admit flat liftings over the Witt vectors together with additional data (logarithmic structure and the Frobenius morphism) by…

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a…

For a prime $p$, a cyclic-by-$p$ group $G$ and a $G$-extension $L|K$ of complete discrete valuation fields of characteristic $p$ with algebraically closed residue field, the local lifting problem asks whether the extension $L|K$ lifts to…

Let $k$ be an algebraically closed complete non-Archimedean field, and let $K$ be a finitely generated field extension over $k$ with transcendence degree $1$. Equip $K$ a non-Archimedean norm extending the one on $k$, and let $\mathcal{K}$…

Suppose $K$ is a finite extension of $\mathbb{Q}_p$ containing a $p^M$-th primitive root of unity. For $1\leqslant s<p$ denote by $K[s,M]$ the maximal $p$-extension of $K$ with the Galois group of period $p^M$ and nilpotent class $s$. We…

We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension $F/\mathbb Q_p$, and an arbitrary finite…

We prove that all endo-$p$-permutation modules for a finite group are liftable from characteristic $p>0$ to characteristic $0$.