On the p-adic Beilinson conjecture for number fields

Details On the p-adic Beilinson conjecture for number fields On the p-adic Beilinson conjecture for number fields

2007-07-25

arxiv.org/abs/0707.3682v2

Mathematics

K-Theory and Homology

Improved presentation of p-adic L-functions; added a remark on the compatibility of the signs between the complex and p-adic r

Scientific paper

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding zeta-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of he conjectures are proved when the number field (or Artin motive) is Abelian over the rationals, and all conjectures are verified numerically in some other cases.

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