Research Field

Arithmetic Geometry

Research Subject

etale cohomology, characteristic cycle, local field, ramification

Current Research

The characteristic cycle of an etale sheaf on an algebraic variety of positive characteristic is defined on the cotangent bundle and satisfies the index formula computing the Euler-Poincare characteristic. The graded quotients of ramification groups of a local field are related to differential forms using blow-up at the ramification divisor in the diagonal of the self product. The characteristic cycle admits a description in terms of the differential forms associated to the character of graded quotients defined by the ramification of the sheaf, on a neighborhood of the generic points of boundary divisor.

Keywords

schemes, sheaves, Galois representations, ramification groups, conductor, Euler-Poincare characteristic

Links

• http://www.ms.u-tokyo.ac.jp/~t-saito