Classification of the Mumford--Tate Groups of Rational Polarizable Hodge Structures
arXiv:2012.14063
Abstract
Let G be the pro-algebraic group attached to the tannakian category of polarizable rational Hodge structures. We show that the quotient of G by its derived group is the Serre group, the derived group of G is the simply connected covering of the adjoint group of G, and that the adjoint group G is a product of specific simple algebraic groups. As the Mumford--Tate groups are exactly the algebraic quotients of G, this also describes them.
11 pages. v2 improved the exposition. arXiv admin note: text overlap with arXiv:1105.0887