Generalized Fesenko reciprocity map

Details Generalized Fesenko reciprocity map Generalized Fesenko reciprocity map

2008-05-22

arxiv.org/abs/0805.3431v1

Mathematics

Number Theory

36 pages. To appear in Algebra i Analiz

Scientific paper

In this paper, which is the natural continuation and generalization of Fesenko's non-abelian reciprocity map, we extend the theory of Fesenko to infinite $APF$-Galois extensions $L$ over a local field $K$, with finite residue-class field $\kappa_K$ of $q=p^f$ elements, satisfying $\pmb{\mu}_p(K^{sep})\subset K$ and $K\subset L\subset K_{\phi^d}$ where the residue-class degree $[\kappa_L:\kappa_K]=d$. More precisely, for such extensions $L/K$, fixing a Lubin-Tate splitting $\phi$ over $K$, we construct a 1-cocycle, \pmb{\Phi}_{L/K}^{(\phi)}:\text{Gal}(L/K)\to K^\times/N_{L_0/K}L_0^\times\times U_{\widetilde{\mathbb X}(L/K)}^\diamond /Y_{L/L_0}, where $L_0=L\cap K^{nr}$, and study its functorial and ramification-theoretic properties. The case $d=1$ recovers the theory of Fesenko.

Affiliated with

Also associated with

No associations

Rating

Generalized Fesenko reciprocity map does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Fesenko reciprocity map, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Fesenko reciprocity map will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-510889