A dynamical systems analogue of Lichtenbaum's recent conjectures on
special values of Hasse-Weil zeta functions
(Un exposé de Christopher Deninger au séminaire de
théorie des nombres de Chevaleret le 27 février 2006)
Résumé :
During the last years, Lichtenbaum has developed conjectures describing
the vanishing orders and values of Hasse-Weil zeta functions at integers in
terms of "Weil-etale cohomologies". These conjectures are substantially
differerent from the Bloch-Kato conjectures and their formalism is simpler.
In the lecture we describe a class of dynamical systems for whose Ruelle
zeta functions a precise analogue of Lichtenbaum's conjectures can be
proven.
The main tools are the Cheeger-Mueller theorem on the equality of analytic
and
combinatorial torsion and certain results in the analysis of foliations.