Shuji Saito

Title: Cohomological Hasse principle and resolution of singularities.

Abstract: In 1985 K.Kato formulated a fascinating framework of conjectures which generalize the Hasse principle for the Brauer group of a number field to the so-called cohomological Hasse principle for a higher dimensional arithmetic scheme. We report on a recent result which proves the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on motivic cohomology, special values of zeta functions, and a geometric application to resolution of singularities.