Department of Mathematics

Student Arithmetic Geometry Seminar

  •  Nick Rekuski, MSU
  •  Perfectoid Fields and Tilting
  •  09/19/2019
  •  10:00 AM - 11:30 AM
  •  C329 Wells Hall

In this talk we will introduce perfectoid fields and tilting. Perfectoid fields provide the the correct base scheme for perfectoid spaces. Tilting is a fundamental tool that will let us lift characteristic $0$ results to characteristic $p$ results. For example, if $K$ is a characteristic $0$ perfectoid field and $K^{\flat}$ is a tilt of $K$ then $K^{\flat}$ is a characteristic $p$ field; $K^{\circ}/K^{\circ\circ}\cong K^{\flat \circ}/K^{\flat\circ\circ}$; if $[L:K]$ is finite then $[L^{\flat}:K^{\flat}]=[L:K]$ (in particular, $L$ is perfectoid); and there is an equivalence of categories between finite étale covers of $K$ and finite étale covers of $K^{\flat}$ via $L\mapsto L^{\flat}$. This talk will not require any material beyond first-year graduate algebra. However, the sophistication required may be higher. To make this talk as accessible as possible, we will include numerous examples.

 

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science