An excursion into p-adic Hodge theory : from foundations to recent trends

0pt20ptINTRODUCTION
AN INTRODUCTION TO HODGE-TATE DECOMPOSITIONS by Gerard Freixas i Montplet
1. Foreword
2. Algebraic and analytic de Rham cohomology
3. Galois cohomology of Cp and its Tate twists
4. Producing p-adic periods from Kähler differentials
5. Hodge-Tate decomposition of abelian varieties
References
AN INTRODUCTION TO p-ADIC PERIOD RINGS by Xavier Caruso
Introduction
1. From Hodge decomposition to Galois representations
2. The first period ring: Cp
3. Two refined period rings: Bcrys and BdR
4. Crystalline and de Rham representations
References
FILTERED (,N)-MODULES AND SEMI-STABLE REPRESENTATIONS by Olivier Brinon
1. Introduction
2. Analogies with the â-adic/complex analytic case
3. The ring Bââ and semi-stable representations
4. The comparison theorem
5. The ð-adic monodromy theorem
6. Appendix: Inputs from log-geometry
References
AN INTRODUCTION TO p-ADIC HODGE THEORY FOR OPEN VARIETIES VIA SYNTOMIC COHOMOLOGY by Go Yamashita
1. Introduction
2. p-adic Hodge theory for proper varieties
3. p-adic Hodge theory for open varieties
References
INTEGRAL p-ADIC HODGE THEORY AND RAMIFICATION OF CRYSTALLINE REPRESENTATIONS by Shin Hattori
1. Introduction
2. Fontaine-Laffaille modules
3. Further developments
4. Sketch of proofs
References
AN INTRODUCTION TO PERFECTOID SPACES by Olivier Brinon, Fabrizio Andreatta, Riccardo Brasca, Bruno Chiarellotto, Nicola Mazzari, Simone Panozzo & Marco Seveso
1. Introduction
2. Motivating problems and constructions
3. Almost mathematics
4. Adic spaces
5. Perfectoid fields and their tilt
6. The relative case: perfectoid spaces and their tilt
7. Comparison theorem for rigid analytic varieties
8. The monodromy-weight conjecture
References