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2009 | 7 | 2 | 206-213
Tytuł artykułu

Ordinary reduction of K3 surfaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
206-213
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
autor
  • Department of Mathematics, Pennsylvania State University, University Park, USA, zarhin@math.psu.edu
Bibliografia
  • [1] Artin M., Supersingular K3 surfaces, Ann. Sci. École Norm. Sup., Sér. 4, 1974, 7, 543–567
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  • [7] Deligne P. (rédigé par L. Illusie), Relèvement des surfaces K3 en charactéristique nulle, In: Surfaces Algébriques, Lecture Notes in Math., Springer, 1981, 868, 58–79 (in French)
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  • [12] Katz N., Messing W., Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math., 1974, 23, 73–77 http://dx.doi.org/10.1007/BF01405203[Crossref]
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  • [15] Mumford D., Abelian varieties, Second Edition, Oxford University Press, London, 1974
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  • [19] Nygaard N., Ogus A., Tate’s conjecture for K3 surfaces of finite height, Ann. of Math., 1985, 122, 461–507 http://dx.doi.org/10.2307/1971327[Crossref]
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  • [22] Serre J.-P., Représentations ℓ-adiques, In: Algebraic number theory (Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ. Kyoto, Kyoto, 1976), 177–193, Japan Soc. Promotion Sci., Tokyo, 1977 (in French)
  • [23] Serre J.-P., Quelques applications du théorème de densité de Chebotarev, Inst. Hautes Études Sci. Publ. Math., 1981, 54, 323–401 (in French) http://dx.doi.org/10.1007/BF02698692[Crossref]
  • [24] Serre J.-P., Abelian ℓ-adic representations and elliptic curves, Second Edition, Addison-Wesley, 1989
  • [25] Skorobogatov A.N., Zarhin Yu.G., A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces, J. Algebraic Geom., 2008, 17, 481–502 [Crossref]
  • [26] Tankeev S.G., On the weights of the ℓ-adic representation and arithmetic of Frobenius eigenvalues, Izv. Ross. Akad. Nauk Ser. Mat., 1999, 63, 185–224 (in Russian), Izv. Math., 1999, 63, 181–218
  • [27] Tate J., Conjectures on algebraic cycles in ℓ-adic cohomology, Motives (Seattle, WA, 1991), 71–83, Proc. Sympos. Pure Math. 55,Part 1, Amer. Math. Soc., Providence, RI, 1994
  • [28] Yu J.-D., Yui N., K3 Surfaces of finite height over finite fields, J. Math. Kyoto Univ., 2008, 48, 499–519
  • [29] Zarhin Yu.G., Hodge groups of K3 surfaces, J. Reine Angew. Math., 1983, 341, 193–220
  • [30] Zarhin Yu.G., Weights of simple Lie algebras in the cohomology of algebraic varieties, Izv. Akad. Nauk SSSR Ser. Mat., 1984, 48, 264–304 (in Russian), Math. USSR Izv., 1985, 24, 245–282
  • [31] Zarhin Yu.G., Transcendental cycles on ordinary K3 surfaces over finite fields, Duke Math. J., 1993, 72, 65–83 http://dx.doi.org/10.1215/S0012-7094-93-07203-1[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0013-8
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