The Mumford-Tate group of 1-motives
نویسندگان
چکیده
منابع مشابه
Mumford-tate Groups
Much of the use of Mumford-Tate groups has been in the classical case of weight one polarized Hodge structures (theory of Shimura varieties). Since this topic will be covered elsewhere in the summer school, this set of lectures will emphasize the non-classical, higher weight case which is much less explored. The first four of these lectures will be largely self-contained, making use of the lect...
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We classify the possible Mumford-Tate groups of polarizable rational Hodge structures.
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We study certain spaces of nilpotent orbits in the Hodge domains introduced by [GGK1], and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these spaces as iteratively fibered algebraic-group orbits in a minimal way.
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Using the ”slice filtration”, defined by effectivity conditions on Voevodsky’s triangulated motives, we define spectral sequences converging to their motivic cohomology and étale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their E2-terms then have a simple description. In particular this yields spectral sequences converging to t...
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A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2002
ISSN: 0373-0956
DOI: 10.5802/aif.1910