Syntomic regulators and special values of \(p\)-adic \(L\)-functions
As a generalization of Leopoldt's \(p\)-adic class number formula, the authors prove \(p\)-adic analogs of the Lichtenbaum conjectures for abelian number fields \(F\), which 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, the \(p\)-adic equivalent of the Beilinson regulator maps, which are compared with etale regulators via the Fontaine-Messing map. Computations of Bloch-Kato when \(p\) is unramified in \(F\) lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.
special values of \(p\)-adic \(L\)-functions
scientific article; zbMATH DE number 1199918