Objectif
The purpose of the project is to develop methods for computing with the rigid and crystalline cohomology of varieties over finite fields. The project will focus on two main problems. First, the fast computation of the Galois action. Second, the effective computation of the cycle class map, and the inverse problem of explicitly recovering algebraic cycles from Galois-invariant cohomology classes (c.f. the Tate conjecture). Research on the first problem would be a natural extension of on-going work of the Prinicipal Investigator and others. By contrast the second problem is entirely new, at least in the context of computational number theory. The overall goal of the project is to provide methods and software which will extend the range of application of computational number theory within the mathematical sciences.
Champ scientifique
Appel à propositions
ERC-2007-StG
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Régime de financement
ERC-SG - ERC Starting GrantInstitution d’accueil
OX1 2JD Oxford
Royaume-Uni