Tate conjecture and mixed perverse sheaves

Details Tate conjecture and mixed perverse sheaves Tate conjecture and mixed perverse sheaves

2006-03-27

arxiv.org/abs/math/0603622v4

Mathematics

Algebraic Geometry

24 pages

Scientific paper

Using the theory of mixed perverse sheaves, we extend arguments on the Hodge conjecture initiated by Lefschetz and Griffiths to the case of the Tate conjecture, and show that the Tate conjecture for divisors is closely related to the de Rham conjecture for nonproper varieties, finiteness of the Tate-Shafarevich groups, and also to some conjectures in the analytic number theory.

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