# Motivic Galois theory for motives of level ≤ 1

Bertolin, Cristiana (2003) Motivic Galois theory for motives of level ≤ 1. arXiv.

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## Abstract

Let T be a Tannakian category over a field k of characteristic 0 and (T) its fundamental group. In this paper we prove that there is a bijection between the otimes-equivalence classes of Tannakian subcategories of T and the normal affine group sub-T-schemes of (T). We apply this result to the Tannakian category T_1(k) generated by motives of niveau 1 defined over k, whose fundamental group is called the motivic Galois group G_mot(T_1(k)) of motives of niveau 1.
We find four short exact sequences of affine group sub-T_1(k)-schemes of G_mot(T_1(k)), correlated one to each other by inclusions and projections. Moreover, given a 1-motive M, we compute explicitly the biggest Tannakian subcategory of the one generated by M, whose fundamental group is commutative.

Item Type:Article
Institutions: Mathematics > Prof. Dr. Uwe Jannsen
Identification Number:
ValueType
arXiv:math/0309379v2arXiv ID
Classification:
NotationType
14L15;18A22MSC
Keywords:Fundamental group of Tannakian categories, Artin motives, 1- motives, motivic Galois groups
Subjects:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Owner:Petra Gürster
Deposited On:27 Nov 2009 08:04
Item ID:10991
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