2010/05/15 by Markus Spitzweck, Spitzweck, Markus
Mathematics · #14F35 #14F42 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14F35 #msc:14F42
paper · pdf · doi:10.48550/arxiv.1005.2670
32 pages, corrected mistake (Lemma 6.10 was incorrect), generalized main statement
arxiv created 2010/11/01 · arxiv updated 2010/11/02
We construct derived fundamental group schemes for Tate motives over connected smooth schemes over fields. We show that there exists a pro affine derived group scheme over the rationals such that its category of perfect representations models the triangulated category of rational mixed Tate motives. Under a hypothesis which is weaker than an integral version of the Beilinson-Soule vanishing conjecture we show that there is an affine derived group scheme over the integers such that its perfect representations model Tate motives with integral coefficients. The hypothesis is for example fulfilled for number fields. This generalizes previous non-derived constructions of fundamental group schemes for Tate motives with rational coefficients.