Section: New Results

p-adic rings and geometry

Participant : Xavier Caruso.

In [19], Xavier Caruso, Tristan Vaccon and Thibaut Verron laid the foundations of an algorithmic treatment of rigid p-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 [22], Xavier Caruso presents a survey on Fontaine's theory of p-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 Bcrys and BdR (and some of their variants) and state several comparison theorems between étale and crystalline or de Rham cohomologies for p-adic algebraic varieties.