Special Values of Zeta-functions and Euler Characteristics


Stephen Lichtenbaum

10:30:00 - 11:30:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Let X be a regular scheme, projective and flat over Spec Z, Let r be a rational integer. We describer a conjecture which gives the value of the zeta function of X at the point s = r in terms of Euler characteristics involving motivic cohomology, Betti cohomology and derived de Rham cohomology. We will explain how this conjecture specializes to known theorems and previous conjectures