East Asian mathematical journal

  • 제30권3호
  • /
  • Pages.321-326
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  • 2014
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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SOME REMARKS ON NON-SYMPLECTIC AUTOMORPHISMS OF K3 SURFACES OVER A FIELD OF ODD CHARACTERISTIC

  • 투고 : 2014.05.04
  • 심사 : 2014.05.16
  • 발행 : 2014.05.31
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초록

In this paper, we present a simple proof of Corollary 3.3 in [5] using the fact that for a K3 surface of finite height over a field of odd characteristic, the height is a multiple of the non-symplectic order. Also we prove for a non-symplectic CM K3 surface defined over a number field the Frobenius invariant of the reduction over a finite field is determined by the congruence class of residue characteristic modulo the non-symplectic order of the K3 surface.

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참고문헌

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  5. Jang, J. The representation of the automorphism groups on the transcendental cycles and the Frobenius invariants of K3 surface, arxiv:1312.7634.
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  8. Nygaard, N.O. Higher De Rham-Witt complexes of supersingular K3 surfaces, Compositio Math. 42, 1981, 245-271.
  9. Nygaard, N.O. and Ogus, A. Tate conjecture for K3 surfaces of finite height, Ann. of Math.(2) 122, 1985, 461-507. https://doi.org/10.2307/1971327
  10. Ogus, A. A crystalline Torelli theorem for supersingular K3 surfaces, Prog. Math. 36, 1983, 361-394.
  11. Rizov, J. Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic, J.reine angew. Math. 648, 2010, 13-67.
  12. Rudakov, A.N. and Shafarevich,I.R. Surfaces of type K3 over fields of finite characteristic, Current problems in mathematics, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii vol. 18, 1981, 115-207.

피인용 문헌

  1. On the Supersingular Reduction of K3 Surfaces with Complex Multiplication vol.2020, pp.20, 2020, https://doi.org/10.1093/imrn/rny210