Vanishing and nilpotence of locally trivial symmetric spaces over regular schemes
نویسندگان
چکیده
منابع مشابه
Rationally trivial quadratic spaces are locally trivial:III
It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R such that q(v) = 0. If char(R) = 2, then in the case of even n we assume that q is a non-singular space in the sense of [Kn] and...
متن کاملFinsler bordifications of symmetric and certain locally symmetric spaces
We give a geometric interpretation of the maximal Satake compactification of symmetric spaces X “ G{K of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable G-invariant Finsler metric on X. As an application, we establish the existence of natural bordifications, as orbifolds-with-corners, of locally symmetric spaces X{Γ for arbitrary discrete subgroups ...
متن کاملTransference principles and locally symmetric spaces
We explain how the Transference Principles from Diophantine approximation can be interpreted in terms of geometry of the locally symmetric spaces Tn = SO(n)\SL(n,R)/SL(n,Z) with n ≥ 2, and how, via this dictionary, they become transparent geometric remarks and can be easily proved. Indeed, a finite family of linear forms is naturally identified to a locally geodesic ray in a space Tn and the wa...
متن کاملThe First Betti Numbers of Certain Locally Trivial Fibre Spaces
The purpose of this department is to provide early announcement of significant new results, with some indications of proof. Although ordinarily a research announcement should be a brief summary of a paper to be published in full elsewhere, papers giving complete proofs of results of exceptional interest are also solicited. Manuscripts more than eight typewritten double spaced pages long will no...
متن کاملGeometric zeta-functions of locally symmetric spaces
The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes the Patterson conjecture. We also extend the range of zeta functions in con...
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: Commentarii Mathematici Helvetici
سال: 2003
ISSN: 0010-2571,1420-8946
DOI: 10.1007/s000140300004