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Non-Archimedean regulator maps and special values of L-functions

Ramesh Sreekantan
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Abstract

We define an analogue of the `Real' Deligne cohomology group at a prime of semi-stable or good reduction of a variety. We also define regulator maps to this group and formulate a conjecture about the image. This allows us to formulate a non-Archimedian version of Beilinson's Hodge-D-conjecture, S-integral and function field versions of Beilinson's global conjectures as well as a precise special value conjecture in the function field case. Finally we give a few examples where these conjectures are known to be true.

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Ramesh Sreekantan. 2003-08-30. Non-Archimedean regulator maps and special values of L-functions. https://arxiv.org/abs/math/0309004

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