nLab Beilinson conjecture



Differential cohomology

Complex geometry



Beilinson’s conjectures (Beilinson 85) conjecture for arithmetic varieties over number fields

  1. that the realification of the Beilinson regulator exhibits an isomorphism between the relevant algebraic K-theory/motivic cohomology groups and Deligne cohomology (ordinary differential cohomology) groups;

    (recalled e.g. as Schneider 88, p. 30, Brylinski-Zucker 91, conjecture 5.20, Deninger-Scholl (3.1.1), Nekovar (6.1 (1))).

  2. induced by this that special values of the (Hasse-Weil-type) L-function are proportional to the Beilinson regulator, in analogy with the class number formula and the Birch and Swinnerton-Dyer conjecture

    (recalled e.g. as Schneider 88, p. 31 Brylinski-Zucker 91, conjecture 5.21, Deninger-Scholl (3.1.2), Nekovar (6.1 (2)))).

The Beilinson conjecture for special values of L-functions follows the Birch and Swinnerton-Dyer conjecture and Pierre Deligne‘s conjecture on special value of L-functions.


The original articles are

Reviews include

Michael Rapoport, Norbert Schappacher, Peter Schneider (eds.), Beilinson's Conjectures on Special Values of L-Functions Perspectives in Mathematics, Volume 4, Academic Press, Inc. 1988 (ISBN:978-0-12-581120-0)

A noncommutative analogue is considered in

Last revised on September 14, 2020 at 07:11:30. See the history of this page for a list of all contributions to it.