Motivic Galois theory for motives of niveau $\leq$ 1

Details Motivic Galois theory for motives of niveau $\leq$ 1 Motivic Galois theory for motives of niveau $\leq$ 1

2003-09-23

arxiv.org/abs/math/0309379v2

Ann. Sci. Math. Qu\'ebec 32 (2008), no. 2, pp. 105--124.

Mathematics

Number Theory

Version with more details

Scientific paper

Let T be a Tannakian category over a field k of characteristic 0 and \pi(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 \pi(T). We apply this result to the Tannakian category T_1(k) generated by motives of niveau \leq 1 defined over k, whose fundamental group is called the motivic Galois group G_mot(T_1(k)) of motives of niveau \leq 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.

Affiliated with

Also associated with

No associations

Rating

Motivic Galois theory for motives of niveau $\leq$ 1 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Motivic Galois theory for motives of niveau $\leq$ 1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Motivic Galois theory for motives of niveau $\leq$ 1 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-182885