Stacky Abelianization of an Algebraic Group

Details Stacky Abelianization of an Algebraic Group Stacky Abelianization of an Algebraic Group

2007-11-19

arxiv.org/abs/0711.3023v2

Mathematics

Algebraic Geometry

22 Pages

Scientific paper

Let G be a connected algebraic group and let [G,G] be its commutator subgroup. We prove a conjecture of Drinfeld about the existence of a connected etale group cover H of [G,G], characterized by the following properties: every central extension of G, by a finite etale group scheme, splits over H, and the commutator map of G lifts to H. We prove, moreover, that the quotient stack of G by the natural action of H is the universal Deligne-Mumford Picard stack to which G maps.

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