On Cyclotomic Numbers and the Reduction Map for the K-Theory of the Integers |
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Authors: | Wojciech Gajda |
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Institution: | (1) Department of Mathematics, Adam Mieckiewicz University, Matejki 48/49, 60769 Pozna, Poland |
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Abstract: | We apply the recently proven compatibility of Beilinson and Soulé elements in K-theory to investigate density of rational primes p, for which the reduction map K
2n+1() K{2n+1}(Fp)is nontrivial. Here n is an even, positive integer and Fp denotes the field of p elements. In the proof we use arithmetic of cyclotomic numbers which come from Soulé elements. Divisibility properties of the numbers are related to the Vandiver conjecture on the class group of cyclotomic fields. Using the K-theory of the integers, we compute an upper bound on the divisibility of these cyclotomic numbers. |
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Keywords: | K-groups special elements cyclotomic fields |
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