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On the Tate conjecture for the Fano surfaces of cubic threefolds. (English) Zbl 1285.14021
Summary: A Fano surface of a smooth cubic threefold $$X\hookrightarrow\mathbb P^4$$ parametrizes the lines on $$X$$. In this note, we prove that a Fano surface satisfies the Tate conjecture over a field of finite type over the prime field and characteristic not 2.

##### MSC:
 14F20 Étale and other Grothendieck topologies and (co)homologies 14F30 $$p$$-adic cohomology, crystalline cohomology 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 14C25 Algebraic cycles 14J45 Fano varieties
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##### References:
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