Sheaf of Modules over $F_1$-schemes

GAP Seminar

Meeting Details

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

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: 106 McAllister

Date: 11/17/2009

Time: 2:30pm - 3:30pm