Mumford-Tate groups of polarizable Hodge structures (Q2814395)

The introduction provides a clear description of the paper: ``This note offers an answer to a question several authors have raised, that of describing which (connected, reductive) algebraic groups over \(\mathbb Q\) can arise as Mumford-Tate groups of polarizable Hodge structures. The study [\textit{M. Green} et al., Mumford-Tate groups and domains. Their geometry and arithmetic. Princeton, NJ: Princeton University Press (2012; Zbl 1248.14001)] made much progress on this question, answering it for simple \(\mathbb Q\)-groups of adjoint type and all absolutely simple \(\mathbb Q\)-groups. We will simplify their arguments in a way that allows for a uniform treatment of the general case. \dots The answer reached is very easy to work with,\dots The techniques of this paper are classical \dots ''