From Wikipedia, the free encyclopedia
Map from algebraic K-theory to cohomology
This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Beilinson regulator" – news · newspapers · books · scholar · JSTOR (April 2023) |
In mathematics, especially in algebraic geometry, the Beilinson regulator is the Chern class map from algebraic K-theory to Deligne cohomology:
Here, X is a complex smooth projective variety, for example. It is named after Alexander Beilinson. The Beilinson regulator features in Beilinson's conjecture on special values of L-functions.
The Dirichlet regulator map (used in the proof of Dirichlet's unit theorem) for the ring of integers of a number field F
is a particular case of the Beilinson regulator. (As usual, runs over all complex embeddings of F, where conjugate embeddings are considered equivalent.) Up to a factor 2, the Beilinson regulator is also generalization of the Borel regulator.
References
[edit]- M. Rapoport, N. Schappacher and P. Schneider, ed. (1988). Beilinson's conjectures on special values of L-functions. Academic Press. ISBN 0-12-581120-9.
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