Sur les extensions intermédiaires des systèmes locaux d'Harris-Taylor
arXiv:1309.5791
Abstract
In the geometric situation of some simple unitary Shimura varieties studied by Harris and Taylor, I have built two filtrations of the perverse sheaf of vanishing cycles. The graduate of the first are the -intermediate extension of some local Harris-Taylor's local systems, while for the second, obtained by duality, they are the -intermediate extensions. In this work, we describe the difference between these and intermediate extension. Precisely, we show, in the case where the local system is associated to an irreducible cuspidal representation whose reduction modulo is supercuspidal, that the two intermediate extensions are the same. Otherwise, if the reduction modulo is just cuspidal, we describe the -torsion of their difference.
28 pages, in French. arXiv admin note: text overlap with arXiv:0707.4396, arXiv:1309.1946