Two lectures about Mumford-Tate groups (Q2898480)
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scientific article; zbMATH DE number 6054505
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two lectures about Mumford-Tate groups |
scientific article; zbMATH DE number 6054505 |
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11 July 2012
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Hodge structures
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Mumford-Tate groups
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elliptic curves
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Two lectures about Mumford-Tate groups (English)
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The author defines Hodge structures as representations of the algebraic group \(\mathbb S\) and introduces the Mumford-Tate group \(\text{MT} (H)\) of a rational Hodge structure \(H\). He provides a characterization of \(\text{MT} (H)\) based on properties of reductive groups and studies it for elliptic curves and their powers. He focuses on cases in which the Hodge struture does not arise from an abelian variety. The paper is based on lectures delivered during the school on Hodge theory held at the CIRM in Trento in August 2009 and includes a set of exercises.
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