Related papers: Packets in Grothendieck's Section Conjecture

In this paper we exhibit the notion of (uniformly) good sections of arithmetic fundamental groups. We introduce and investigate the problem of cuspidalisation of sections of arithmetic fundamental groups, its ultimate aim is to reduce the…

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.

We formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k satisfies the section conjecture. We prove many cases of…

In this article we introduce and study a motivic category in the arithmetic of function fields, namely the category of motives over an algebraic closure $L$ of a finite field with coefficients in a global function field over this finite…

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on…

We show that the existence of rational points on smooth varieties over a field can be detected using homotopy fixed points of etale topological types under the Galois action. As our main example we show that the surjectivity statement in…

In this paper we deal with Grothendieck's interpretation of Artin's interpretation of Galois's Galois Theory (and its natural relation with the fundamental group and the theory of coverings) as he developed it in Expose V, section 4,…

We establish that the Grothendieck-Teichmuller conjecture, which predicts an isomorphism between the Grothendieck-Teichmuller group GT and the absolute Galois group of rational numbers Gal, holds in the setting of profinite spaces. To…

The Grothendieck universe axiom asserts that every set is a member of some set-theoretic universe U that is itself a set. One can then work with entities like the category of all U-sets or even the category of all locally U-small…

For a given arithmetic scheme, in this paper we will introduce and discuss the monodromy action on a universal cover of the \'etale fundamental group and the monodromy action on an \emph{sp}-completion constructed by the graph functor,…

Field Arithmetic studies the interplay between arithmetical properties of fields and their absolute Galois groups. Here we studies fields satisfying local global principles for rational points of varieties and profinite groups satisfying…

We prove the local Gross-Prasad conjecture for generic L-packets of representations of special orthogonal groups. The proof uses the same result for tempered L-packets proved in a preceding paper, and irreducibility results for the induced…

Let $X$ be a smooth projective curve of genus $\geq2$ over a number field. A natural variant of Grothendieck's Section Conjecture postulates that every section of the fundamental exact sequence for $X$ which everywhere locally comes from a…

A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an…

In a series of papers [Pan0], [Pan1], [Pan2], [Pan3] we give a detailed and better structured proof of the Grothendieck--Serre's conjecture for semi-local regular rings containing a finite field. The outline of the proof is the same as in…

The Elementary Type Conjecture in Galois theory provides a concrete inductive description of the finitely generated maximal pro-$p$ Galois groups $G_F(p)$ of fields $F$ containing a root of unity of order $p$. We describe several variants…

In this paper we prove that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives) in each pair. The algebraic and topological approaches to…

In this note, we explore the notion of hyperbolicity of topologically finitely generated profinite groups. Some applications to diophantine geometry are suggested and we try to reformulate certain problems in diophantine geometry in terms…

In their study of Arthur's conjectures for real groups, Adams, Barbasch, and Vogan introduced the notion of micro-packets. Micro-packets are finite sets of irreducible representations defined using microlocal geometric methods and…

In this paper we prove Vogan's conjecture on local Arthur packets, for Arthur parameters of $p$-adic general linear groups that are irreducible as representations of $W_F \times SL_2(\mathbb{C}) \times SL_2(\mathbb{C})$ - we refer to such…