Noncommutative Geometry Seminar

The well-known analytic class number formula, linking the special value at s=0 of the Dedekind zeta function of a number field to its class number and regulator, has been the foundation and prototype for the highly conjectural theory of special values of L-functions. We will discuss generalizations of the class number formula to the context of equivariant Artin L-functions which capture refinements of the Brumer-Stark and the Coates-Sinnott conjectures, as well as the Iwasawa main conjecture. These generalizations relate various algebraic-geometric invariants associated to a global field, e.g. its Quillen K-groups and etale cohomology groups, to various special values of its Galois-equivariant L-functions. They illustrate the subtle interactions of number theory with complex and p-adic analysis, algebraic geometry, topology and homological algebra.