## Seminar on Arithmetic Algebraic Geometry: Syntomic cohomology

Date
2012-1-12 13:30 - 2012-1-12 16:30
Place
Faculty of Science Building #3 Room 413
Speaker/Organizer
Masanori Asakura

This is an expository talk on syntomic cohomology of Fontaine and
Messing, which is the key tool in the proof of the comparison theorems in p-adic Hodge theory.
Starting from the definition of syntomic complex, I will explain how to relate etale cohomology to filtered $\phi$-module (Fontaine-Messing theory).
If time permits, I will also explain explicit reciprocity law of Kato.
(I am sorry I cannot explain log-syntomic or rigid syntomic cohomology
because I am a poor mathematician.)