Bertolin, Cristiana (2003) Motivic Galois theory for motives of level ≤ 1. arXiv.
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.
|Institutions:||Mathematics > Prof. Dr. Uwe Jannsen|
|Keywords:||Fundamental group of Tannakian categories, Artin motives, 1- motives, motivic Galois groups|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||27 Nov 2009 07:04|
|Last Modified:||08 Oct 2012 06:58|