Related papers: On just infinite pro-p-groups and arithmetically p…

We extend the work of Pappas-Rapoport-Zhu on twisted affine Grassmannians to wildly ramified, quasi-split, and residually split groups, assuming the maximal torus is induced. This relies on the construction, inspired by Tits, of certain…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

Let $F$ be a number field and $p$ an odd prime. We estimate the kernels and cokernels of the codescent maps of the \'etale wild kernels over various $p$-adic Lie extensions. For this, we propose a novel approach of viewing the \'etale wild…

We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect…

We study dp-minimal infinite profinite groups that are equipped with a uniformly definable fundamental system of open subgroups. We show that these groups have an open subgroup $A$ such that either $A$ is a direct product of countably many…

We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known…

Suppose $\mathcal K$ is $N$-dimensional local field of characteristic $p$, $\mathcal G =\mathop{Gal}(\mathcal K_{sep}/\mathcal K)$, $\mathcal G_{<p}$ is the maximal quotient of $\mathcal G$ of period $p$ and nilpotent class $<p$ and…

Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…

For a finite totally ramified extension $L$ of a complete discrete valuation field $K$ with the perfect residue field of characteristic $p>0$, it is known that $L/K$ is an abelian extension if the upper ramification breaks are integers and…

We consider the isomonodromic deformations of irregular-singular connections defined on principal bundles over complex curves: for any complex reductive structure group G, and any polar divisor; allowing for a twisted/ramified formal normal…

Proofs that an arbitrary field has a separable closure are necessarily non-constructive, and separable closures are unique only up to non-canonical isomorphism. This means that the absolute Galois group of a field is defined only up to…

This work examines the commutator structure of some closed subgroups of the wild group of automorphisms of a local field with perfect residue field, a group we call $\Cal J.$ In particular, we establish a new approach to evaluating…

Let $F$ be a characteristic zero differential field with algebraically closed constant field, and consider the compositum $F_u$ of all Picard--Vessiot extensions of $F$ with unipotent differential Galois group. We prove that the group of…

The tame Gras-Munnier Theorem gives a criterion for the existence of a ${\mathbb Z}/{\mathbb Z}$-extension of a number field $K$ ramified at exactly a set $S$ of places of $K$ prime to $p$ (allowing real Archimedean places when $p=2$) in…

Let L/K be a finite Galois extension of complete local fields with finite residue fields and let G=Gal(L/K). Let G_1 and G_2 be the first and second ramification groups. Thus L/K is tamely ramified when G_1 is trivial and we say that L/K is…

We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.

This article is concerned with proving a refined function field analogue of the Coates-Sinnott conjecture, formulated in the number field context in 1974. Our main theorem calculates the Fitting ideal of a certain even Quillen K-group in…

We study the asymptotic distribution of wildly ramified extensions of function fields in characteristic $p > 2$, focusing on (certain) $p$-groups of nilpotency class at most $2$. Rather than the discriminant, we count extensions according…

Given a Galois cover of curves over $\mathbb{F}_p$, we relate the $p$-adic valuation of epsilon constants appearing in functional equations of Artin L-functions to an equivariant Euler characteristic. Our main theorem generalises a result…

In this paper we study formal moduli for wildly ramified Galois covering. We prove a local-global principle. We then focus on the infinitesimal deformations of the Z/pZ-covers. We explicitly compute a deformation of an automorphism of order…