# The Galois group of the category of mixed Hodge-Tate structures

Research paper by Alexander Goncharov, Guangyu Zhu

Indexed on: 23 May '17Published on: 23 May '17Published in: arXiv - Mathematics - Algebraic Geometry

#### Abstract

The category of rational mixed Hodge-Tate structures is a mixed Tate category. Therefore thanks to the Tannakian formalism, it is equivalent to the category of finite dimensional graded comodules over a graded commutative Hopf algebra H over Q. Since the category has homological dimension 1, the Hopf algebra H is isomorphic to the commutative graded Hopf algebra provided by the tensor algebra of the graded vector space given by the direct sum of the groups C/Q(n) over n>0. However this isomorphism is not natural in any sense, e.g. does not work in families. We give a different natural explicit construction of the Hopf algebra H.