ar X iv : 0 70 9 . 19 79 v 1 [ m at h . A G ] 1 3 Se p 20 07 K 3 Surfaces of Finite Height over Finite Fields ∗ †
نویسندگان
چکیده
Arithmetic of K3 surfaces defined over finite fields are investigated. In particular, we show that any K3 surface X of finite height over a finite field k of characteristic p ≥ 5 has a quasi-canonical lifting Z to characteristic 0, and that the endormorphism algebra of the transcendental cycles V (Z), as a Hodge module, is a CM field over Q. We also prove the Tate conjecture for any powers of such a K3 surface over k when the lifted Frobenius on V (Z) is irreducible. We illustrate by examples how to determine the associated formal Brauer group explicitly. Examples discussed here are all of hypergeometric type.
منابع مشابه
ar X iv : 0 70 9 . 19 79 v 3 [ m at h . A G ] 1 4 O ct 2 00 7 K 3 Surfaces of Finite Height over Finite Fields ∗ †
Arithmetic of K3 surfaces defined over finite fields are investigated. In particular, we show that any K3 surface X of finite height over a finite field k of characteristic p ≥ 5 has a quasi-canonical lifting Z to characteristic 0, and that for any such Z, the endormorphism algebra of the transcendental cycles V (Z), as a Hodge module, is a CM field over Q. We illustrate by examples how to dete...
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