Related papers: The arithmetic local Nori fundamental group

In this note we generalize Nori's definition of the fundamental group scheme from a rational point to an arbitrary base point so that when we take $X$ to be a field $k$ and the point to be $k\subseteq \bar{k}$ we still get a non trivial…

For $X$ a complete, reduced, geometrically connected scheme over a perfect field of characteristic $p>0$, we analyze the decomposition of Nori's fundamental group scheme into its local and \'etale parts and raise the question of the…

We give a condition that ensures that a fibered category over a field admits a universal morphism to a profinite gerbe. This fundamental gerbe generalizes both Nori's fundamental group scheme and Deligne's relative fundamental groupoid.…

We introduce three notion of tameness of the Nori fundamental group scheme for a normal quasiprojective variety $X$ over an algebraically closed field. It is proved that these three notions agree if $X$ admits a smooth completion with…

We define a linear structure on Grothendieck's arithmetic fundamental group $\pi_1(X, x)$ of a scheme $X$ defined over a field $k$ of characteristic 0. It allows us to link the existence of sections of the Galois group ${\rm Gal}(\bar k/k)$…

In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic…

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…

Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $A$ be an abelian surface over $k$. Fix an integer $n \geq 1$ such that $p \nmid n$ and let $K^{[n]}$ be the $n$-th Generalized Kummer Variety associated to $A$. In…

In this article, we study the log-scheme theoretic version of the Nori fundamental group scheme. Similar to the classical Nori fundamental group scheme, the log Nori fundamental group scheme classifies torsors on log flat topology. We also…

Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…

Given an algebraic stack, we compare its Nori fundamental group with that of its coarse moduli space. We also study conditions under which the stack can be uniformized by an algebraic space.

We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…

We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and…

A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p\ne 0$ and the category of absolute Galois groups of fields $K$…

In this paper we will define a qc fundamental group for an arithmetic scheme by quasi-galois closed covers. Then we will give a computation for such a group and will prove that the etale fundamental group of an arithmetic scheme is a normal…

We generalize the logarithmic purity theorem of Fujiwara-Kato to torsors which arise in the Kummer log flat topology under finite flat linearly reductive group schemes. As an application, we construct the logarithmic Nori fundamental group…

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a…

In this paper, we study a certain extension of Nori's fundamental group in the case where a base field is of characteristic 0 and give structure theorems about it. As a result, for a smooth projective curve with genus $g$>1, we prove that…

Let $K$ be a number field and $S$ a set of primes of $K$. We write $K_S/K$ for the maximal extension of $K$ unramified outside $S$ and $G_{K,S}$ for its Galois group. In this paper, we prove the following generalization of the…

We show that for any given field $k$ and natural number $r\geq2$, every continuous extension of the absolute Galois group $\mathrm{Gal}_k$ by a finite group is the arithmetic fundamental group of a geometrically connected smooth projective…