ISSN:
1573-0514
Keywords:
K 2
;
Galois cohomology
;
descent
;
number fields
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Description / Table of Contents:
Abstract LetF be a field andE/F be a Galois extension with groupG. In this paper, we establish canonical isomorphisms: $$\begin{gathered} Ker(K_2 (F) \to K_2 (E)^G ) \cong H^1 (G,K_3 (E_0 )_{ind} ); \hfill \\ Coker(K_2 (F) \to K_2 (E)^G ) \cong H^2 (G,K_3 (E_0 )_{ind} ), \hfill \\ \end{gathered} $$ whereE 0 is the field of constants ofE andK 3(E 0)ind is the indecomposable quotient ofK 3(E 0). We exploit these isomorphisms in various situations: general fields, function fields of varieties, number fields.
Notes:
Résumé SoientF un corps commutatif etE/F une extension galoisienne de groupeG. Le but de cet article est d'établir et d'exploiter dans diverses situations des isomorphismes canoniques: $$\begin{gathered} Ker(K_2 (F) \to K_2 (E)^G ) \cong H^1 (G,K_3 (E_0 )_{ind} ); \hfill \\ Coker(K_2 (F) \to K_2 (E)^G ) \cong H^2 (G,K_3 (E_0 )_{ind} ), \hfill \\ \end{gathered} $$ oùE 0 est le corps des constantes deE etK 3(E 0)ind est le quotient indécomposable deK 3(E 0).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00962794
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