scholarly journals On the Galois and flat cohomology of unipotent algebraic groups over local and global function fields. I

2008 ◽  
Vol 319 (10) ◽  
pp. 4288-4324 ◽  
Author(s):  
Nguyêñ Quôć Thǎńg ◽  
Nguyêñ Duy Tân
Keyword(s):  
Function Fields ◽  
Algebraic Groups ◽  
Global Function ◽  
Global Function Fields ◽  
Unipotent Algebraic Groups

scholarly journals Finite presentability of arithmetic groups over global function fields

1987 ◽  
Vol 30 (1) ◽  
pp. 23-39 ◽  
Author(s):  
Helmut Behr
Keyword(s):  
Small Groups ◽  
Function Fields ◽  
Algebraic Groups ◽  
Number Fields ◽  
Arithmetic Groups ◽  
Finitely Generated ◽  
Global Function ◽  
Global Function Fields ◽  
Finite Presentability ◽  
Finitely Presented

Arithmetic subgroups of reductive algebraic groups over number fields are finitely presentable, but over global function fields this is not always true. All known exceptions are “small” groups, which means that either the rank of the algebraic group or the set S of the underlying S-arithmetic ring has to be small. There exists now a complete list of all such groups which are not finitely generated, whereas we onlyhave a conjecture which groups are finitely generated but not finitely presented.

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