NDLI: Finiteness theorems for algebraic groups over function fields

Content Provider	Scilit
Author	Conrad, Brian
Copyright Year	2011
Description	Journal: Compositio Mathematica 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 semi-simple groups via systematic use of the recently developed structure theory and classification of pseudo-reductive groups.
Ending Page	639
Starting Page	555
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x11005665
Journal	Compositio Mathematica
Issue Number	2
Volume Number	148
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2011-11-30
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Finiteness theorems for algebraic groups over function fields