## Student Arithmetic Geometry Seminar

•  Nick Rekuski, MSU
•  Fargues-Fontaine Curve: Part I
•  04/12/2019
•  2:00 PM - 4:00 PM
•  C204A Wells Hall

There is a close analogy between function fields over finite fields and number fields. In this analogy $\text{Spec } \mathbb{Z}$ corresponds to an algebraic curve over a finite field. However, this analogy often fails. For example, $\text{Spec } \mathbb{Z} \times \text{Spec } \mathbb{Z}$ (which should correspond to a surface) is $\text{Spec } \mathbb{Z}$ (which corresponds to a curve). In many cases, the Fargues-Fontaine curve is the natural analogue for algebraic curves. In this first talk, we will give the construction of the Fargues-Fontaine curve.

## Contact

Department of Mathematics
Michigan State University