Rigid syntomic cohomology

General Introduction
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Online References
MR1809626 (2002c:14035) Besser, Amnon(4DRHM) Syntomic regulators and $p$adic integration. I. Rigid syntomic regulators. First paragraph of review: For (possibly nonproper) smooth schemes over a $p$adic field with good reduction, the author constructs a theory of rigid syntomic cohomology, which is a $p$adic analogue of the Deligne cohomology. This theory is based on P. Berthelot's rigid cohomology [Invent. Math. 128 (1997), no. 2, 329377; MR1440308 (98j:14023)], in the same way as the Deligne cohomology is based on the de Rham/Hodge cohomology. He also constructs a syntomic regulator from $K$theory to his rigid syntomic cohomology, which is an analogue of Beilinson's regulator. Probably one may expect to formulate a $p$adic version of the Beilinson conjecture, which should predict a relation between special values of $p$adic $L$functions and his syntomic regulator. The author obtains a result in this direction for CM elliptic curves [Part II, Israel J. Math. 120 (2000), part B, 335359; MR1809627 (2002c:14036); see the following review].
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
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