Abstract.
In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map, and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.
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Oblatum 14-V-96 & 9-X-97
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Kolster, M., Do, T. Syntomic regulators and special values of p-adic L-functions. Invent math 133, 417–447 (1998). https://doi.org/10.1007/s002220050250
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DOI: https://doi.org/10.1007/s002220050250