The third (and the last) volume of the Proceedings of the p-adic semester at Institut Poincaré in 1997 contains two long articles. The first, by J.-M. Fontaine, treats several topics from the theory of p-adic Galois representations: Sen's theory of C-representations, its generalization to BdR -representations, sketch of the proof by Colmez and Fontaine of the fundamental conjecture “weakly admissible implies admissible”, some remarks on the period rings. The second article is the long-awaited paper of K. Kato, which concludes the proof of one of the most spectacular number theoretical results from the 1990's, namely “one half” of the Main Conjecture of Iwasawa Theory for classical modular forms and its applications to the p-adic conjecture of Birch and Swinnerton-Dyer (and its generalizations).

Reviewer:

jnek