Generalized logarithmic derivatives for K_n

Details Generalized logarithmic derivatives for K_n Generalized logarithmic derivatives for K_n

2006-11-06

arxiv.org/abs/math/0611136v1

Mathematics

Number Theory

34 pages

Scientific paper

We construct (generalized) logarithmic derivatives for general n-dimensional local fields K of mixed characteristics (0,p) in which p is not necessarily a prime element with residue field k such that [k:k^p]=p^{n-1}. For the construction of the logarithmic derivative map, we define n-dimensional rings of overconvergent series and show that - as in the 1-dimensional case - they can be interpreted as functions converging on some annulus of the open unit p-adic disc. Using the generalized logarithmic derivative, we give a new construction of Kato's n-dimensional dual exponential map.

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