Objective
We will consider a field K with an operator of one of the following 4 kinds: derivation, automorphism, Hasse derivation and derivation of Frobenius. We are interested in results of two kinds -- geometric and model theoretical (i.e. concerning first-order properties of those structures).
First, I explain what kind of geometric results we expect. For an algebraic variety X (or scheme) over K, we enrich the geometry of X by extending the operator to the structure sheaf of X. In the case of a derivation such an enriched geometric structure is called (Buium) a D-variety. We want to extend Buium's results about D-varieties (as description of D-groups or isotriviality of projective D-varieties) into a wider class of geometric objects where the operator is one of the remaining 3 kinds.
The results already obtained (by Buium for derivations and by Anand Pillay and me for automorphisms) yield diophantine consequences in the style of the Mordell-Lang conjecture. We hope that an analysis of the remaining cases yields similar consequences. From the logical standpoint, we will study the first-order properties of the above geometric structures. We are interested in quantifier elimination results, i.e. in deciding the combinatorial complexity of the definable sets there.
Another goal is to study the first order properties of the field with an operator itself. There is a great deal of work already done in the cases of derivations, automorphism and Hasse derivations but the case of derivations of Frobenius was only treated b y me in one paper. So, we want to continue working on model theory of fields with derivations of Frobenius (e.g. work out the theory of definable groups there).
The last thing to be done is studying the limit theory of derivation of Frobenius when the power of Frobenius map grows to infinity (i.e. we get the theory of derivation of nonstandard Frobenius). We would like to prove that this theory is related to e.c. fields with a derivation of an endomorphism.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics geometry
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2002-MOBILITY-5
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.