For more information about this meeting, contact Nigel Higson, Ping Xu, Mathieu Stienon.
| Title: | Sheaf of Modules over $F_1$-schemes |
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| Seminar: | GAP Seminar |
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| Speaker: | Chenghao Chu, Johns Hopkins University |
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| Abstract: |
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| 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 |
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| Date: | 11 / 17 / 2009 |
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| Time: | 02:30pm - 03:30pm |
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