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Effective methods in rigid and crystalline cohomology

Objective

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.

Call for proposal

ERC-2007-StG
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Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 750 000
Principal investigator
Alan George Beattie Lauder (Dr.)
Administrative Contact
Stephen Conway (Dr.)

Beneficiaries (1)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
EU contribution
€ 750 000
Address
Wellington Square University Offices
OX1 2JD Oxford
Activity type
Higher or Secondary Education Establishments
Principal investigator
Alan George Beattie Lauder (Dr.)
Administrative Contact
Stephen Conway (Dr.)