m at h . A G ] 1 M ay 2 00 8 K 3 Surfaces of Finite Height over Finite Fields ∗ †
نویسندگان
چکیده
Arithmetic of K3 surfaces defined over finite fields is 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. The Tate conjecture for the product of certain two K3 surfaces is also proved. We illustrate by examples how to determine explicitly the formal Brauer group associated to a K3 surface over k. 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...
متن کاملar 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 ∗ †
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 s...
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