数論幾何学セミナー De Rham-Witt complexes and p-adic Hodge theory (3)

開催日時
2011年   3月 16日 14時 00分 ~ 2011年   3月 16日 16時 00分
場所
北大理学部3号館413室
講演者
Luc Illusie (Université Paris-Sud)
 
The subject of p-adic Hodge theory is the study of the relations between de Rham, crystalline, and p-adic tale cohomology over discrete valuation rings of mixed characteristic (0, p). A key technical tool in this study is the theory of the de Rham-Witt complex. After a brief historical introduction I will recall the basics of :
• Witt vectors
• crystalline cohomology
• de Rham-Witt complexes.
I will then discuss applications of the de Rham-Witt theory to
• slopes of Frobenius
• log crystalline cohomology and the Hyodo-Kato isomorphism.
Finally, I will briefly discuss
• Fontaine’s period isomorphisms.
To conclude, I will present a recent arithmetic application of the whole theory,
due to P. Berthelot, H. Esnault and K. Rlling.

関連項目

研究集会・セミナー・集中講義の一覧へ