# zbMATH — the first resource for mathematics

Higher fields of norms and $$(\varphi,\Gamma)$$-modules. (English) Zbl 1186.11070
In this article, the author gives a generalization of Fontaine and Wintenberger’s theory of the “field of norms” for local fields with imperfect residue fields (admitting a finite $$p$$-basis). After that, he studies the theory of $$(\varphi,\Gamma)$$-modules in this setting and proves an analogue of Herr’s formulas for the cohomology of $$p$$-adic Galois representations. The author’s constructions do not use higher ramification theory (used by Fontaine and Wintenberger and more recently Abrashkin), but instead use the differential characterization of deeply ramified extensions.

##### MSC:
 11S15 Ramification and extension theory 11S23 Integral representations 11S25 Galois cohomology 12G05 Galois cohomology
##### Keywords:
local fields; ramification theory; Galois representations
Full Text: