Seminar on Arithmetic Algebraic Geometry:Riemann-Roch theorem for logarithmic schemes

2013-10-18 10:00 - 2013-10-18 16:00
Faculty of Science Building #3 Room 413
The Riemann-Roch theorem is a fundamental tool for the computation of

cohomological invariants of algebraic varieties or complex manifolds,

and plays an essential role in various fields of mathematics,

such as complex analysis, algebraic geometry and number theory.

In the fifties this theorem is reformulated and generalised by Grothendieck

in terms of K-groups,and even now many mathematicians yield lots of variants,

together with a wide range of applications.

In this talk, we survey speaker's research on a generalisation of the

theorem to logarithmic varieties (in the sense of Fontaine-Illusie-Kato)

formulated by using a log-geometric variant of K-groups - a Kummer etale

K-group, and give its application to number theory.