Christophe Breuil: Splitting and Making Explicit the de Rham Complex of the Drinfeld Space, Kartoniert / Broschiert

Klappentext

This book gives a complete description of the de Rham complex of the Drinfeld space of dimension n − 1 as a complex of representations of GL*~n~* (K ), where n ≥ 2 and K is a finite field extension of the field of p -adic numbers. The group GL*~n~* (K ) acts on the Drinfeld space of dimension n − 1, hence on its complex of differential forms, yielding representations of GL*~n~* (K ) that mathematicians began to study in the 1980s. Understanding these representations was one of the main motivations for the development of the theory of locally analytic representations of GL*~n~* (K ), which can be seen as a p -adic analogue of Harish-Chandra's (gl*~n~* ,K )-modules (in the latter, K is a maximal compact subgroup of GL*~n~*(R)).

A transparent description is provided of the global sections of the de Rham complex of the Drinfeld space of dimension n -1 as a complex of (duals of) locally analytic representations of GL*~n~* (K ), and an explicit partial splitting of this complex is constructed in the derived category of (duals of) locally analytic representations of GL*~n~* (K). Multiple intermediate results on Ext groups of locally analytic representations are established, which may be useful in other contexts. Requiring a light background in locally analytic representations, modules over enveloping algebras, and rigid spaces, the book is aimed at a general audience of number theorists and representation theorists.