Local-global principles for homogeneous spaces of reductive groups over global function fields
نویسندگان
چکیده
Let X be a homogeneous space of reductive group with stabilizers, defined over global field positive characteristic. Using duality theorems for complexes tori, we study cohomological obstructions to various arithmetic properties.
منابع مشابه
Reductive Groups over Fields
These are lecture notes that Tony Feng live-TEXed from a course given by Brian Conrad at Stanford in“winter” 2015, which Feng and Conrad edited afterwards. Two substitute lectures were delivered (by Akshay Venkatesh and Zhiwei Yun) when Conrad was out of town. This is a sequel to a previous course on the general structure of linear algebraic groups; some loose ends from that course (e.g., Cheva...
متن کاملFiniteness properties of soluble arithmetic groups over global function fields
Let G be a Chevalley group scheme and B ≤ G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K , and OS be the corresponding S–arithmetic ring. Then, the S– arithmetic group B(OS) is of type F |S|−1 but not of type FP |S| . Moreover one can derive lower and upper bounds for the geometric invariants Σ(B(OS)). These are sha...
متن کاملCycle groups of curves over global fields
The purpose of this investigation is to study certain low-dimensional cycle groups of smooth projective curves over global fields of positive characteristic, that is, fields which are finitely generated of transcendence degree one over a finite field. After a brief introduction, we overview some established results in this area and extend them appropriately. Throughout this paper, an algebraic ...
متن کاملCriterion for proper actions on homogeneous spaces of reductive groups
Let M be a manifold, on which a real reductive Lie group G acts transitively. The action of a discrete subgroup Γ on M is not always properly discontinuous. In this paper, we give a criterion for properly discontinuous actions, which generalizes our previous work [6] for an analogous problem in the continuous setting. Furthermore, we introduce the discontinuous dual t(H:G) of a subset H of G , ...
متن کاملDimension data, and Local versus Global Conjugacy in Reductive Groups
Let G be a reductive algebraic group and H be a connected semisimple subgroup of G. The dimension data consists of the collection { dimV H } with V H denoting the space of points in V fixed by H , and where (ρ, V ) runs through all representations of G. One may ask if the dimension data determine H up to conjugacy or at least isomorphism. In other words, If H and H ′ have the same dimension dat...
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 Henri Lebesgue
سال: 2022
ISSN: ['2644-9463']
DOI: https://doi.org/10.5802/ahl.144