Affine Deligne–lusztig Varieties at Infinite Level (preliminary Version)
نویسنده
چکیده
Part 1. Two analogues of Deligne–Lusztig varieties for p-adic groups 5 2. Affine Deligne–Lusztig varieties at infinite level 5 2.1. Preliminaries 5 2.2. Deligne–Lusztig sets/varieties 7 2.3. Affine Deligne–Lusztig varieties and covers 8 2.4. Scheme structure 9 3. Case G = GLn, b basic, w Coxeter 12 3.1. Notation 12 3.2. Basic σ-conjucacy classes. Isocrystals 12 3.3. The admissible subset of Vb and F -cyclic lattices 12 3.4. Comparison and uniformization of DLV and ADLV 13 3.5. Connected components 17
منابع مشابه
Affine Deligne-lusztig Varieties in Affine Flag Varieties
This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.
متن کاملConnected Components of Affine Deligne-lusztig Varieties in Mixed Characteristic
We determine the set of connected components of minuscule affine Deligne-Lusztig varieties for special maximal compact subgroups of unramified connected reductive groups. Partial results are also obtained for non-minuscule closed affine Deligne-Lusztig varieties. We consider both the function field case and its analog in mixed characteristic. In particular, we determine the set of connected com...
متن کاملConnected Components of Closed Affine Deligne-lusztig Varieties
We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-d...
متن کاملThe Dimension of Some Affine Deligne-lusztig Varieties
We prove Rapoport’s dimension conjecture for affine Deligne-Lusztig varieties for GLh and superbasic b. From this case the general dimension formula for affine DeligneLusztig varieties for special maximal compact subgroups of split groups follows, as was shown in a recent paper by Görtz, Haines, Kottwitz, and Reuman.
متن کاملThe Cohomology of Semi-infinite Deligne–lusztig Varieties
We prove a 1979 conjecture of Lusztig on the cohomology of semi-infinite Deligne– Lusztig varieties attached to division algebras over local fields. We also prove the two conjectures of Boyarchenko on these varieties. It is known that in this setting, the semi-infinite Deligne–Lusztig varieties are ind-schemes comprised of limits of certain finite-type schemes Xh. Boyarchenko’s two conjectures ...
متن کامل