A Cohomological Approach to Properties of the Norm Residue Symbol in Higher Dimensional Class Eld Theory
نویسنده
چکیده
In earlier work the author proved that the Vostokov symbol of the n-dimensional mixed characteristic local eld X n = kfft 1 n) q ! q commutes with the corresponding Vostokov symbol of X n?1 = kfft 1 gg : : :fft n?2 gg. Here the author generalizes this theorem to the case of a regular local ring A subject to certain conditions. This is done by using Kato's reformulation of the Vostokov symbol as a map from Milnor K-theory to Fontaine-Messing cohomology.
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تاریخ انتشار 2007