By Sophie Morel
This ebook stories the intersection cohomology of the Shimura types linked to unitary teams of any rank over Q. regularly, those forms will not be compact. The intersection cohomology of the Shimura kind linked to a reductive staff G contains commuting activities of absolutely the Galois workforce of the reflex box and of the crowd G(Af) of finite adelic issues of G. the second one motion may be studied at the set of complicated issues of the Shimura sort. during this e-book, Sophie Morel identifies the Galois action--at strong places--on the G(Af)-isotypical parts of the cohomology.
Morel makes use of the strategy built by way of Langlands, Ihara, and Kottwitz, that's to match the Grothendieck-Lefschetz mounted element formulation and the Arthur-Selberg hint formulation. the 1st challenge, that of employing the mounted aspect formulation to the intersection cohomology, is geometric in nature and is the article of the 1st bankruptcy, which builds on Morel's earlier paintings. She then turns to the group-theoretical challenge of evaluating those effects with the hint formulation, whilst G is a unitary team over Q. functions are then given. specifically, the Galois illustration on a G(Af)-isotypical section of the cohomology is pointed out at just about all locations, modulo a non-explicit multiplicity. Morel additionally provides a few effects on base switch from unitary teams to common linear groups.
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