Open AccessA note on the cohomology of the Langlands group
Author(s) -
Edward S. T. Fan
Publication year - 2014
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2014-06230-2
Subject(s) - cohomology , mathematics , spectral sequence , group (periodic table) , dimension (graph theory) , class (philosophy) , exact sequence , pure mathematics , algebra over a field , artificial intelligence , computer science , physics , quantum mechanics
We begin with a comparison of various cohomology theories for topological groups. Using the continuity result for Moore cohomology, we establish a Hochschild-Serre spectral sequence for a slightly larger class of groups. We use these properties to compute the cohomology of the Langlands group of a totally imaginary field. The appendix answers a question raised by Flach concerning the cohomological dimension of the group R \mathbb {R} .