We develop a general theory of mixed Hodge structures over local
or global function fields which in many ways resembles the formalism of
classical Hodge structures. Our objects consist of a finite dimensional
vector space together with a weight filtration, but instead of a Hodge
filtration we require finer information. In order to obtain a reasonable
category we impose a semistability condition in the spirit of invariant
theory and prove that the resulting category is tannakian. This allows us
to define and analyze Hodge groups and determine them in some cases.
The analogies with classical mixed Hodge structures range from the
role of semistability to the fact that both objects arise from the analytic
behavior of motives. The precise relation of our objects with the analytic
uniformization of Anderson's -motives will be the subject of a separate
paper. For Hodge structures arising from Drinfeld modules we can combine the present results with a previous one on Galois representations,
obtaining a precise analogue of the Mumford-Tate conjecture.
Dieser Eintrag ist Teil der Universitätsbibliographie.
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