The geometric Satake correspondence for ramified groups
نویسندگان
چکیده
منابع مشابه
Geometric Satake, Springer Correspondence, and Small Representations
For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...
متن کاملGeometric Satake, Springer Correspondence, and Small Representations Ii
Abstract. For a split reductive group scheme Ǧ over a commutative ring k with Weyl group W , there is an important functor Rep(Ǧ, k) → Rep(W, k) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dua...
متن کاملTwisted Geometric Satake Equivalence
Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → Gm → E → G(F) → 1, any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN (k) → Q ∗ l (under some assumption on the characteristic of k). Consider the category of G(O)biinvariant perverse sheaves on E wi...
متن کاملLocal models for ramified unitary groups
S′ −−−−→ Spec(OE) is cartesian. To qualify as a model, the scheme S′ should at least be flat over Spec(OE) and have only “good” singularities. In the PEL-case, S can be written as a moduli space of abelian varieties with polarization, an action by a semisimple Q-algebra and a K-level strucure where K ⊂ G(Af ) is an open and compact subgroup. If we fix a prime p , the investigation of a model S′...
متن کاملAffine Grassmannians and the Geometric Satake in Mixed Characteristic
We endow the set of lattices in Qp with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2015
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2248