WEC&DS

Weil-étale cohomology and Deninger's dynamical system

Coordinatore	WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER    more  Organization address address: SCHLOSSPLATZ 2 city: MUENSTER postcode: 48149 contact info Titolo: Dr. Nome: Katharina Cognome: Steinberg Email: send email Telefono: +49 2518322154 Fax: +49 2518321501
Nazionalità Coordinatore	Germany [DE]
Totale costo	161˙769 €
EC contributo	161˙769 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2009-IEF
Funding Scheme	MC-IEF
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-10-15   -   2011-11-14

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	WESTFAELISCHE WILHELMS-UNIVERSITAET MUENSTER  Organization address address: SCHLOSSPLATZ 2 city: MUENSTER postcode: 48149 contact info Titolo: Dr. Nome: Katharina Cognome: Steinberg Email: send email Telefono: +49 2518322154 Fax: +49 2518321501	DE (MUENSTER)	coordinator	161˙769.00

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 Obiettivo del progetto (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.'