Asymptotic cohomology of circular units
BELLIARD, Jean-Robert
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Mathématiques de Bordeaux [IMB]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Mathématiques de Bordeaux [IMB]
BELLIARD, Jean-Robert
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
International Journal of Number Theory. 2009-11p. 1205-1219
World Scientific Publishing
English Abstract
Let $F$ be a number field, abelian over the rational field, and fix a odd prime number $p$. Consider the cyclotomic $Z_p$-extension $F_\infty/F$ and denote $F_n$ the ${n}^{\rm th}$ finite subfield and $C_n$ its group of ...Read more >
Let $F$ be a number field, abelian over the rational field, and fix a odd prime number $p$. Consider the cyclotomic $Z_p$-extension $F_\infty/F$ and denote $F_n$ the ${n}^{\rm th}$ finite subfield and $C_n$ its group of circular units. Then the Galois groups $G_{m,n}=\Gal(F_m/F_n)$ act naturally on the $C_m$'s (for any $m\geq n>> 0$). We compute the Tate cohomology groups $\Hha^i(G_{m,n}, C_m)$ for $i=-1,0$ without assuming anything else neither on $F$ nor on $p$.Read less <
Origin
Hal imported