L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld
In the context of the local Langlands correspondence, a geometric relation between the Lubin-Tate tower and the Drinfeld tower has long been expected. The recent book “L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld” of Laurent Fargues, Alain Genestier and Vincent Lafforgue makes this relation explicit. Read the elaborated review of Elmar Große-Klönne in Zbl 1136.14001 to get acquainted with the sophisticated mathematics involved.
“The book aims to be self contained, proofs are given in full detail. The inputs needed from Dieudonné theory (crystals), Rapoport-Zink period spaces and period maps, (rig)-étale sheaf- and topos theory, equivariant cohomology etc. are carefully presented in various appendices to the main text, complemented by various useful digressions. Thus, the reader finds a wealth of valuable material on many topics related to the proper subject of this book. To anyone working on p-adic period spaces, p-adic moduli spaces or geometric aspects on the local Langlands program this book can highly be recommended.”