scholarly journals Abelian extensions of global fields with constant local degree

2006 ◽  
Vol 13 (4) ◽  
pp. 599-605 ◽  
Author(s):  
Hershy Kisilevsky ◽  
Jack Sonn
Keyword(s):  
Abelian Extensions ◽  
Global Fields ◽  
Local Degree

On the different of abelian extensions of global fields

1992 ◽  
pp. 26-32 ◽  
Author(s):  
Gerhard Frey ◽  
Marc Perret ◽  
Henning Stichtenoth
Keyword(s):  
Abelian Extensions ◽  
Global Fields

scholarly journals Abelian extensions and crossed modules of Hom-Lie algebras

2020 ◽  
Vol 224 (3) ◽  
pp. 987-1008
Author(s):  
José Manuel Casas ◽  
Xabier García-Martínez
Keyword(s):  
Lie Algebras ◽  
Abelian Extensions ◽  
Crossed Modules

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

Embeddings of maximal tori in classical groups over local and global fields

2016 ◽  
Vol 80 (4) ◽  
pp. 17-34 ◽  
Author(s):  
Eva Bayer-Fluckiger ◽  
Eva Bayer-Fluckiger ◽  
Ting-Yu Lee ◽  
Ting-Yu Lee ◽  
Raman Parimala ◽  
...  
Keyword(s):  
Classical Groups ◽  
Global Fields ◽  
Maximal Tori

Reduction theory over global fields

1994 ◽  
Vol 104 (1) ◽  
pp. 207-216 ◽  
Author(s):  
T. A. Springer
Keyword(s):  
Reduction Theory ◽  
Global Fields
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