On the Tate conjecture for the Fano surfaces of cubic threefolds

Details On the Tate conjecture for the Fano surfaces of cubic threefolds On the Tate conjecture for the Fano surfaces of cubic threefolds

2012-03-13

arxiv.org/abs/1203.2913v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

The Fano surface of a smooth cubic threefold F in mathbb{P}^{4} parametrizes the lines on F. We prove that a Fano surface verify the Tate conjecture over finite fields and number fields. We give an algorithm to compute the zeta function of the intermediate Jacobian of a cubic over a finite field and we compute the zeta function of various examples of Fano surfaces. We obtain some examples of Fano surfaces with supersingular reduction.

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