THE EXPLICIT RECIPROCITY LAW OF BLOCH-KATO

We give a detailed account of the ''fundamental exact sequence'', which is basic to understanding the ring B-cris (both B-cris and the fundamental exact sequence are due to Fontaine). We present a proof of the explicit reciprocity law of Bloch and Kato, which is somewhat different than the original one. We then discuss the possibility of extending there results to Lubin-Tate groups of height > 1.