PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Ping Xu, Mathieu Stienon.

Title:Sheaf of Modules over $F_1$-schemes
Seminar:GAP Seminar
Speaker:Chenghao Chu, Johns Hopkins University
Abstract:
Using Connes and Consani’s definition of F1 -schemes, we define and study the category of coherent sheaves over an F1 -scheme. We show that exact sequences of locally free modules are well defined in the category of coherent sheaves over an F1 -scheme. We then apply Q-construction to define algebraic K-theory of F1 -schemes. In partic- ular, we show that the algebraic K-groups of S pec(F1 ) are the stable homotopy groups of the sphere $S^0$ , which is generally believed to be true. If time permits, we define algebraic K-theory of not necessarily commutative monoids. In particular, we discuss the homotopy invari- ance property of algebraic K-theory of monoids and F1 -schemes.

Room Reservation Information

Room Number:MB106
Date:11 / 17 / 2009
Time:02:30pm - 03:30pm