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 |