Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0708.4034

Tate motives and the fundamental group

Hélène Esnault·Marc Levine
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let k be a number field, and let S be a finite set of k-rational points of P^1. We relate the Deligne-Goncharov contruction of the motivic fundamental group of X:=P^1_k- S to the Tannaka group scheme of the category of mixed Tate motives over X.

Explore related subjects

math.AGmath.KT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hélène Esnault, Marc Levine. 2007-08-29. Tate motives and the fundamental group. https://arxiv.org/abs/0708.4034

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A cluster criterion for potential degeneracy of superelliptic curves

Let $K$ be a field with a discrete valuation; let $p$ be a prime; and let $C$ be the curve defined by an equation of the form $y^p = f(x)$. We show that the curve $C$ has a model over an algebraic extension of $K$ whose special fiber consists of genus-$0$ components and has at worst nodal singularities if and only if the cluster data of the roots of $f$ satisfies a certain criterion, and when these hold, we show explicitly how to build the minimal regular model of $C$. We develop an interpretation of cluster data in terms of a convex hull in the Berkovich projective line and express the above results directly in terms of this convex hull.

math.AG↗
arXiv2026

A note on complex Lie Algebras isomorphic to their conjugate

A real Lie algebra defines by extension of scalars a complex Lie algebra that is isomorphic to its Galois conjugate. In this paper, we are interested in the converse property: given a complex Lie algebra that is isomorphic to its conjugate, is it defined over the real numbers? We prove the existence of a $10$-dimensional nilpotent complex Lie algebra for which the answer is negative, disproving a recent conjecture by Deré. In addition, we compute the generic obstruction to this descent problem in terms of Brauer groups.

math.AG↗