Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Special Values of Zeta-functions and Euler Characteristics
Stephen Lichtenbaum (Brown University)
Let X be a regular scheme, projective and flat over Spec Z, let r be a rational integer. We describe 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.