The fundamental group of period domains over finite fields
نویسندگان
چکیده
منابع مشابه
The Fundamental Group of Period Domains over Finite Fields
We determine the fundamental group of period domains over finite fields. This answers a question of M. Rapoport raised in [R].
متن کاملDeligne-lusztig Varieties and Period Domains over Finite Fields
Let G0 be a reductive group over Fq. There are two classes of algebraic varieties over an algebraic closure F of Fq attached to G0. Let us recall their definition. We set G = G0×Fq F. To G there is associated the maximal torus, the Weyl group W and the set of fundamental reflections in W , cf. [DL] 1.1. Let X = XG be the set of all Borel subgroups of G. Then X is a smooth projective algebraic v...
متن کاملThe cohomology of period domains for reductive groups over finite fields
Let k = Fq be a finite field and G a reductive algebraic group defined over k of semisimple rank d := rkss(G) resp. semisimple k-rank d ′ := k-rkss(G). Fix a pair T ⊂ B consisting of a maximal torus T and a Borel subgroup B both defined over k. We denote by R the roots, by R the positive roots and by ∆ = {α1, . . . , αd} the base of simple roots with respect to T ⊂ B. Let k a finite field exten...
متن کاملThe Automorphism Group over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq, if looked at as bijections Fq −→ Fq , give all possible bijections in case q = 2, or q = p where p > 2. In case q = 2 where r > 1 it is shown that the tame subgroup of the invertible polynomial maps give only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fq can be a zero set...
متن کاملThe continuous cohomology of period domains over local fields
In this paper we consider period domains over local fields for quasi-split reductive groups. We compute the continuous l-adic cohomology with compact support of them in the case of a basic isocrystal. This paper is a continuation of [O2] where we considered the étale cohomology with torsion coefficients of these spaces. AMS 2000 Mathematics subject classification: Primary 14L05. Secondary 14G22...
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: Advances in Mathematics
سال: 2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.06.011