منابع مشابه
Finiteness theorems for algebraic groups over function fields
We prove the finiteness of class numbers and Tate-Shafarevich sets for all affine group schemes of finite type over global function fields, as well as the finiteness of Tamagawa numbers and Godement’s compactness criterion (and a local analogue) for all such groups that are smooth and connected. This builds on the known cases of solvable and semisimple groups via systematic use of the recently ...
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The first section of this paper provides an improvement upon known finiteness theorems for Riemannian submersions; that is, theorems which conclude that there are only finitely many isomorphism types of fiber bundles among Riemannian submersions whose total spaces and base spaces both satisfy certain geometric bounds. The second section of this paper provides a sharpening of some recent theorem...
متن کاملSome Finiteness Theorems for Abelian Varieties
Last time we saw (see Proposition 6.5 in those lecture notes) that an abelian variety A of dimension g over K, the fraction field of a henselian dvr R, acquires semistable reduction over K(A[`]) for ` equal to 4 or an odd prime, with ` not divisible by the residue characteristic. (The same circle of ideas yielded the non-obvious fact that over K the intersection of two “semistable field extensi...
متن کاملFiniteness Theorems for the Shifted Witt and Higher Grothendieck-witt Groups of Arithmetic Schemes
For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher GrothendieckWitt groups (aka Hermitian K-theory) of curves are finitely generated. For more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck-Witt gr...
متن کاملFiniteness of Class Numbers for Algebraic Groups
Let G be an affine group scheme of finite type over a global field F . (We do not assume G to be reductive or smooth or connected.) Let AF denote the locally compact adele ring of F , S be a finite non-empty set of places of F that contains the archimedean places, and AF the factor ring of adeles with vanishing component along S; for FS = ∏ v∈S Fv, we have AF = FS ×AF . Recall that if X is a fi...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1979
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1979-14630-5