Section: New Results
-adic rings and geometry
Participant : Xavier Caruso.
In , Xavier Caruso, Tristan Vaccon and Thibaut Verron laid the foundations of an algorithmic treatment of rigid -adic geometry by introducting and studing Gröbner bases over Tate algebras. In addition, they designed a Buchberger-like and a F4-like algorithm for computing such Gröbner bases.
In , Xavier Caruso presents a survey on Fontaine's theory of -adic period rings. These notes are based on a course given jointly by Laurent Berger and Xavier Caruso in Rennes in 2014; their aim is to detail the construction of the rings and (and some of their variants) and state several comparison theorems between étale and crystalline or de Rham cohomologies for -adic algebraic varieties.