Colloquium

Thursday, Sep. 20, 2007

4:00 PM, BAC 219

Speaker: Kimberly Retert, Miami University, Oxford, Ohio

Visiting Assistant Professor

Title:  Curve Categories in Grothendieck Categories

Abstract:  Noncommutative projective geometry, inspired by the success of commutative

projective geometry, attempts to understand noncommutative graded rings by applying

techniques, ideas and/or intuitions of traditional algebraic geometry.  One successful

approach, based on Serre's Theorem, is to use categories, specifically Grothendieck

categories, in the place of the topological spaces called varieties.  A next step in this

approach is to examine analogues of subvarieties.  After a brief overview of the pertinent

part of commutative projective geometry---and why the obvious generalization does not

work---this talk will discuss ``curve categories," one way to generalize the idea of curves

on a space to the categorical setting, and some conditions when these curve categories can

be described