Witt Rings and Galois Groups

1996 ◽  
Vol 144 (1) ◽  
pp. 35 ◽  
Author(s):  
Jan Minac ◽  
Michel Spira
Keyword(s):  
Galois Groups ◽  
Witt Rings

Decomposition of Witt Rings and Galois Groups

1995 ◽  
Vol 47 (6) ◽  
pp. 1274-1289 ◽  
Author(s):  
Ján Mináč ◽  
Tara L. Smith
Keyword(s):  
Galois Group ◽  
Group Ring ◽  
Galois Groups ◽  
Complete List ◽  
Direct Products ◽  
Free Products ◽  
Basic Part ◽  
Witt Ring ◽  
Semidirect Products ◽  
Witt Rings

AbstractTo each field F of characteristic not 2, one can associate a certain Galois group 𝒢F, the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction of Witt rings corresponds to semidirect products of W-groups, and the basic part of W(F) is related to the center of 𝒢F. In an appendix we provide a complete list of Witt rings and corresponding w-groups for fields F with |Ḟ/Ḟ2| ≤ 16.

scholarly journals On the Cohomology of Galois Groups Determined by Witt Rings

1999 ◽  
Vol 148 (1) ◽  
pp. 105-160 ◽  
Author(s):  
Alejandro Adem ◽  
Dikran B Karagueuzian ◽  
Ján Mináč
Keyword(s):  
Galois Groups ◽  
Witt Rings

Free pro- $p$ product decompositions of Galois groups

1997 ◽  
Vol 225 (2) ◽  
pp. 245-261 ◽  
Author(s):  
Ido Efrat
Keyword(s):  
Galois Groups

On the calculation of some differential galois groups

1987 ◽  
Vol 87 (1) ◽  
pp. 13-61 ◽  
Author(s):  
Nicholas M. Katz
Keyword(s):  
Galois Groups
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