Seminar on Arithmetic Algebraic Geometry:RiemannRoch theorem for logarithmic schemes
 Date

20131018 10:00 
20131018 16:00
 Place
 Faculty of Science Building #3 Room 413

Speaker/Organizer
 Kei HAGIHARA

 The RiemannRoch 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 Kgroups,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 FontaineIllusieKato)
formulated by using a loggeometric variant of Kgroups  a Kummer etale
Kgroup, and give its application to number theory.