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Formal hodge structures : dottorato di ricerca in matematica : tesi di dottorato

Mazzari, Nicola <1979- >

Tesi o dissertazioni - 2009

The aim of this work is to develop the program proposed by S. Bloch, L. Barbieri-Viale and V. Srinivas of generalizing Deligne mixed Hodge structures providing a new cohomology theory for complex algebraic varieties. In other words to construct and study cohomological invariants of (proper and complex) algebraic schemes which are finer than the associated mixed Hodge structures in the case of singular spaces. Chapter 1. We give a survey on the theory of 1-motives starting from the original work of Deligne. Then we recall the theory of Laumon 1-motives and we prove that the cohomological dimension of the category of Laumon 1-motives up to isogenies is one following the proof of Orgogozo for Deligne 1-motives. Chapter 2. This is the core of this work. We develop the theory of formal Hodge structures (of level $\le n$). In particular we extend to this setting some of the notions of the theory of 1-motives. We give some results in order to compute the ext-groups of formal Hodge structures. [...]
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D. 2009 0282
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