Asymptotic cohomology of circular units

Details Asymptotic cohomology of circular units Asymptotic cohomology of circular units

2007-11-19

arxiv.org/abs/0711.2739v1

International Journal of Number Theory (2009) 1205-1219

Mathematics

Number Theory

Scientific paper

10.1142/S179304210900264X

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 $p$.

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