Related papers: Log Fundamental Group Scheme

We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…

Given a Henselian and Japanese discrete valuation ring $A$ and a flat and projective $A$-scheme $X$, we follow the approach of Biswas-dos Santos to introduce a full subcategory of coherent modules on $X$ which is then shown to be Tannakian.…

We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded…

We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated…

We first show that every group-theoretical category is graded by a certain double coset ring. As a consequence, we obtain a necessary and sufficient condition for a group-theoretical category to be nilpotent. We then give an explicit…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

This article studies an extended Nori and local fundamental group schemes of Abelian varieties. We also discuss the birational invariance of these group schemes and study their behaviour under the Albanese and \'{e}tale morphisms.

We solve the following algorithmic problems using TC0 circuits, or in logspace and quasilinear time, uniformly in the class of nilpotent groups with bounded nilpotency class and rank: subgroup conjugacy, computing the normalizer and…

Let $X$ be a smooth projective curve over the complex numbers. We compute the Brauer group of the moduli stack of Bruhat-Tits group scheme $\mathcal{G}$-torsors on $X$. When $g(X) \geq 3$ we compute the Brauer group of the regularly stable…

We show that Nori's fundamental group scheme \pi(X,x) does not base change correctly under extension of the base field for certain smooth projective ordinary curves X of genus 2 defined over a field of characteristic 2.

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…

By developing a theory of deformations over nilpotent Lie algebras, based on Schlessinger's deformation theory over Artinian rings, this paper investigates the pro-l-unipotent fundamental group of a variety X. If X is smooth and proper,…

In this article, we introduce an approach to study the fundamental group of a log terminal T-variety. As applications, we prove the simply connectedness of the spectrum of the Cox ring of a complex Fano variety, we compute the fundamental…

In this paper we will give the computation of the etale fundamental group of an arithmetic scheme.

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…

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.

It is known that the fundamental groups of smooth loci of Log del Pezzo Surfaces are finite groups. The aim of this note is to study these finite groups. A short table containing these groups is given. And lots of groups on the table are…

Using log convergent topoi, %In the derived category of filtered complexes of %sheaves of modules over %an isostructure we define two fundamental filtered complexes $(E_{conv},P)$ and $(C_{conv},P)$ for the log scheme obtained by a smooth…

We present an algorithm which determines the fundamental group of a spatial section using topspin networks. Tracking the topology of the spatial section is a unique feature of this approach, which is not possible in standard Loop Quantum…