Series: Mathematics Colloquium

Date: Thursday, March 28, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Yuri Zarhin

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Aleksey Parshin (Steklov Institute, Moscow)

Title: Local Constructions in Algebraic Geometry

Abstract: 

The talk will contain an elementary introduction to the theory of
n-dimensional local fields and its applications.  This theory extends
to higher dimensions the classical local-to-global principle known in
algebraic number theory and complex analysis.  The typical example of
an n-dimensional local field is the field of iterated Laurent power
series.  Such constructions as the residue from analysis or tame
symbol from number theory can be developed for schemes of higher
dimension using the technics of higher local fields.