Objective
The aim of our research proposal is to study the connections between Lichtenbaum's Weil-étale cohomology and Deninger's dynamical system. Weil-étale cohomology (respectively Deninger's program) is meant to provide an arithmetic cohomology (respectively a geometric cohomology) relevant for the study of motivic L-functions. These are two very ambitious and promising directions in arithmetic geometry, which are certainly strongly related even if these connections are not well understood. According to Deninger's program, a foliated dynamical system should be attached to an arithmetic scheme. This dynamical system would produce Deninger's conjectural cohomological formalism. On the other hand, Lichtenbaum predicts the existence of a Weil-étale cohomology theory for arithmetic schemes allowing a cohomological interpretation for the special values of the corresponding zeta functions. This conjectural Weil-étale cohomology should be the cohomology of a deeper topological structure, namely the conjectural Weil-étale topos. The Weil-étale topos is naturally defined in characteristic p while an unsatisfactory definition has been given for number rings and more generally for arithmetic schemes. This Weil-étale topos, i.e. this generalized space, turns out to be closely related to Deninger's dynamical system. We propose to use topos theory in order to study simultaneously the Weil-étale topos and Deninger's dynamical system. The insight provided by Deninger's work will be applied to obtain new results in Weil-étale cohomology. Respectively, Lichtenbaum's explicit computations will be used to obtain information on Deninger's dynamical system. The ultimate goal of this research project is to define and study the conjectural Weil-étale topos in characteristic zero. One interesting aspect of this project is the interaction of general topos theory and dynamical systems with more classical and well etablished number theory, such as the analytic class number formula.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciencesmathematicsapplied mathematicsdynamical systems
- natural sciencesmathematicspure mathematicsgeometry
- natural sciencesmathematicspure mathematicsarithmeticsL-functions
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Topic(s)
Call for proposal
FP7-PEOPLE-2009-IEF
See other projects for this call
Funding Scheme
MC-IEF - Intra-European Fellowships (IEF)Coordinator
48149 MUENSTER
Germany