m at h . A G ] 1 M ay 2 00 8 K 3 Surfaces of Finite Height over Finite Fields ∗ †

نویسندگان

  • J. - D. Yu
  • N. Yui
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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

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 ∗ †

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...

متن کامل

8 M ay 2 00 8 SCHUR – WEYL DUALITY OVER FINITE FIELDS

We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has more than r elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if dimV is at least r + 1 then the natural map kSr → EndGL(V )(V ) is an isomorphism; this isomorphism may fail if dimk(V ) is not strictly larger than r.

متن کامل

ar X iv : m at h / 06 05 44 4 v 1 [ m at h . N T ] 1 6 M ay 2 00 6 ABELIAN VARIETIES OVER CYCLIC FIELDS

Let K be a field of characteristic 6= 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense in A. Unless K ⊂ F̄p for some p, the rank of A over K is infinite.

متن کامل

8 M ay 2 00 2 On finite congruence - simple semirings ∗

In this paper, we describe finite, additively commutative, congruence simple semirings. The main result is that the only such semirings are those of order 2, zeromultiplication rings of prime order, matrix rings over finite fields, and those that are additively idempotent.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008