منابع مشابه
A Cohomological Approach to Properties of the Norm Residue Symbol in Higher Dimensional Class Eld Theory
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...
متن کاملCalculating the Power Residue Symbol and Ibeta
In the recent PhD thesis of Bouw, an algorithm is examined that computes the group structure of the principal units of a p-adic number eld completion. In the same thesis, this algorithm is used to compute Hilbert norm residue symbols. In the present paper, we will demonstrate two other applications. e rst application is the computation of an important invariant of number eld completions, ca...
متن کاملThe Norm Residue Isomorphism Theorem
We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).
متن کاملAn Efficient Seventh Power Residue Symbol Algorithm
Power residue symbols and their reciprocity laws have applications not only in number theory, but also in other fields like cryptography. A crucial ingredient in certain public key cryptosystems is a fast algorithm for computing power residue symbols. Such algorithms have only been devised for the Jacobi symbol as well as for cubic and quintic power residue symbols, but for no higher powers. In...
متن کاملAxioms for the Norm Residue Isomorphism
We give an axiomatic framework for proving that the norm residue map is an isomorphism (i.e., for settling the motivic Bloch-Kato conjecture). This framework is a part of the Voevodsky-Rost program.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2001
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa98-1-3