Studio Phones Seminar

Workshop of F-purity and related topics

Date:
2012/03/05
Place:
Division of Human Environment, Graduate School of Human Development and Environment, Kobe University. (No. 10 at the Campus Map)
Room:
A739
Organizers:
Yusuke Kiriu (Studio Phones), Kosaku Nagasaka (Kobe University)
time:
1000-1130
title:
Local fields and its arithmetic
speaker:
Kazuma Shimomoto (Meiji Univetisty)
abstract:

A typical example of a local field is constructed as the completion of the field of rationals Q with respect to a fixed valuation on Q. I will talk about a classification theorem of local fields due to Ostrowski and see that the metric defined on a non-archimedean local field looks different from the Euclidean metric. As an application, we will discuss when a given quadratic form has a rational solution. If time permits, we would like to mention Hilbert symbols and quaternion algebras.

Reference: Serre, Local fields, Springer

time:
15:00 - 16:00
title:
Category theory and its applications to rings and singularity
speaker:
Daisuke Hirose (Hokkaido University)
abstract:

In this talk, I discuss an application of category theory to rings and singularities. This will provide subtle information of commutative rings of positive characteristic. Our target is a singularity called F-pure. I also introduce new definition of F-purity.

time:
16:10 - 17:10
title:
Characteristic p method for singularity theory
speaker:
Keiichi Watanabe (Nihon University)
abstract:

In this talk, I will show how to compute lc-thresholds of a singularity or how to prove that certain singularity is a rational singularity or not by characteristic p method by the examples of rational double points and jet schemes.