Mumford-Tate groups of polarizable Hodge structures

TL;DR

This paper classifies the Mumford-Tate groups associated with polarizable rational Hodge structures and explores their connection to a conjectural property of motivic Galois groups, providing new insights into Hodge theory and motives.

Contribution

It offers a classification of Mumford-Tate groups for polarizable Hodge structures and establishes a Hodge-theoretic analogue of a conjecture related to motivic Galois groups.

Findings

Classification of Mumford-Tate groups achieved

A polarized Hodge-theoretic analogue of Serre's conjecture proposed

New connections between Hodge theory and motivic Galois groups established

Abstract

We classify the possible Mumford-Tate groups of polarizable rational Hodge structures. Along the way we deduce a polarized Hodge-theoretic analogue of a conjectural property of motivic Galois groups suggested by Serre.