Le théorème de MacIntyre sur les ensembles définissables dans les corps -adiques
Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients
Let be a finite extension of . The field of norms of a -adic Lie extension is a local field of characteristic which comes equipped with an action of . When can we lift this action to characteristic , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of -modules, and give a condition for the existence of certain types of lifts.
We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].