By Sophie Morel
This booklet reviews the intersection cohomology of the Shimura forms linked to unitary teams of any rank over Q. mostly, those kinds aren't compact. The intersection cohomology of the Shimura type linked to a reductive staff G includes commuting activities of absolutely the Galois staff of the reflex box and of the crowd G(Af) of finite adelic issues of G. the second one motion will be studied at the set of advanced issues of the Shimura type. during this booklet, Sophie Morel identifies the Galois action--at solid places--on the G(Af)-isotypical elements of the cohomology.
Morel makes use of the strategy constructed by means of Langlands, Ihara, and Kottwitz, that is to check the Grothendieck-Lefschetz mounted aspect formulation and the Arthur-Selberg hint formulation. the 1st challenge, that of utilising the mounted aspect formulation to the intersection cohomology, is geometric in nature and is the thing 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, while G is a unitary staff over Q. purposes are then given. specifically, the Galois illustration on a G(Af)-isotypical portion of the cohomology is pointed out at just about all areas, modulo a non-explicit multiplicity. Morel additionally offers a few effects on base switch from unitary teams to common linear groups.
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