메뉴 건너뛰기




Volumn 9, Issue 2, 2000, Pages 355-393

Liftings of simple normal crossing log K3 and log Enriques surfaces in mixed characteristics

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034421043     PISSN: 10563911     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (28)

References (50)
  • 1
    • 0009214312 scopus 로고
    • Formal groups arising from algebraic varieties
    • e série, tome 10 (1977), 87-132.
    • (1977) e Série , vol.10 , pp. 87-132
    • Artin, M.1    Mazur, B.2
  • 2
    • 0003339375 scopus 로고
    • Surfaces algébriques complexes
    • Soc. Math. de France
    • A. Beauville, Surfaces algébriques complexes, Astérisque 54, Soc. Math. de France, 1978.
    • (1978) Astérisque , vol.54
    • Beauville, A.1
  • 3
    • 0003343964 scopus 로고
    • Cohomologie cristallline des schémas de caractéristique p > 0
    • Springer-Verlag, New York
    • P. Berthelot, Cohomologie cristallline des schémas de caractéristique p > 0, Lecture Notes in Math. 407, Springer-Verlag, New York, 1974.
    • (1974) Lecture Notes in Math. , vol.407
    • Berthelot, P.1
  • 5
    • 0000493498 scopus 로고
    • F-Isocrystals and de Rham cohomology I
    • P. Berthelot and A. Ogus, F-Isocrystals and de Rham cohomology I, Invent. Math. 72 (1983), 159-199.
    • (1983) Invent. Math. , vol.72 , pp. 159-199
    • Berthelot, P.1    Ogus, A.2
  • 7
    • 0040078933 scopus 로고
    • Relèvement des surfaces K3 en caractéristique nulle
    • Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Springer-Verlag, New York
    • P. Deligne, Relèvement des surfaces K3 en caractéristique nulle, In: Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Lecture Notes in Math. 868, Springer-Verlag, New York, 1981, pp. 58-79.
    • (1981) Lecture Notes in Math. , vol.868 , pp. 58-79
    • Deligne, P.1
  • 8
    • 0010896111 scopus 로고
    • Cristaux ordinaire et coordonnées canoniques
    • Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Springer-Verlag, New York
    • P. Deligne and L. Illusie, Cristaux ordinaire et coordonnées canoniques, In: Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Lecture Notes in Math. 868, Springer-Verlag, New York, 1981, pp. 80-127.
    • (1981) Lecture Notes in Math. , vol.868 , pp. 80-127
    • Deligne, P.1    Illusie, L.2
  • 11
    • 0002633804 scopus 로고
    • Global smoothings of varieties with normal crossings
    • R. Friedman, Global smoothings of varieties with normal crossings, Ann. of Math. 118 (1983), 75-114.
    • (1983) Ann. of Math. , vol.118 , pp. 75-114
    • Friedman, R.1
  • 12
    • 0346502084 scopus 로고
    • Type III degenerations of K3 surfaces
    • R. Friedman and F. Scattone, Type III degenerations of K3 surfaces, Invent. Math. 83 (1983), 1-39.
    • (1983) Invent. Math. , vol.83 , pp. 1-39
    • Friedman, R.1    Scattone, F.2
  • 13
    • 0003322387 scopus 로고
    • Algebraic geometry
    • Springer-Verlag, New York
    • R. Hartshorne, Algebraic geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, 1977.
    • (1977) Graduate Texts in Math. , vol.52
    • Hartshorne, R.1
  • 14
    • 0001543630 scopus 로고
    • Semi-stable reduction and crystalline cohomology with logarithmic poles
    • Périodes p-adiques, Séminaire de Bures, 1988. Soc. Math. de France
    • O. Hyodo and K. Kato, Semi-stable reduction and crystalline cohomology with logarithmic poles, In: Périodes p-adiques, Séminaire de Bures, 1988. Astérisque 223, Soc. Math. de France (1994), 221-268.
    • (1994) Astérisque , vol.223 , pp. 221-268
    • Hyodo, O.1    Kato, K.2
  • 15
    • 34250284984 scopus 로고
    • On the periods of Enriques surfaces I
    • E. Horikawa, On the periods of Enriques surfaces I, Math. Ann. 234 (1978), 73-88.
    • (1978) Math. Ann. , vol.234 , pp. 73-88
    • Horikawa, E.1
  • 16
    • 0000614668 scopus 로고
    • A note on p-adic étale cohomology in the semi-stable reduction case
    • O. Hyodo, A note on p-adic étale cohomology in the semi-stable reduction case, Invent. Math. 91 (1988), 543-557.
    • (1988) Invent. Math. , vol.91 , pp. 543-557
    • Hyodo, O.1
  • 17
    • 0000500378 scopus 로고
    • Complexe de de Rham-Witt et cohomologie cristalline
    • e série 12 (1979), 501-661.
    • (1979) e Série , vol.12 , pp. 501-661
    • Illusie, L.1
  • 18
    • 0039544464 scopus 로고
    • Ordinarité des intersections complètes générales
    • Progress in Math. 87 Birkhäuser
    • L. Illusie, Ordinarité des intersections complètes générales, In: The Grothendieck Festschrift Vol. II, Progress in Math. 87 Birkhäuser, 1990, pp. 375-407.
    • (1990) The Grothendieck Festschrift , vol.2 , pp. 375-407
    • Illusie, L.1
  • 19
    • 0000591805 scopus 로고
    • Réduction semi-stable ordinaire, cohomologie étale p-adique et cohomologie de de Rham d'aprés Bloch [BK] et Hyodo [H]
    • Périodes p-adiques, Séminaire de Bures, 1988. Soc. Math. de France
    • L. Illusie, Réduction semi-stable ordinaire, cohomologie étale p-adique et cohomologie de de Rham d'aprés Bloch [BK] et Hyodo [H], In: Périodes p-adiques, Séminaire de Bures, 1988. Astérisque 223, Soc. Math. de France (1994), 209-220.
    • (1994) Astérisque , vol.223 , pp. 209-220
    • Illusie, L.1
  • 20
    • 0030304025 scopus 로고    scopus 로고
    • Log smooth deformation theory
    • F. Kato, Log smooth deformation theory, Tôhoku Math. Jour. 48 (1996), 317-354.
    • (1996) Tôhoku Math. Jour. , vol.48 , pp. 317-354
    • Kato, F.1
  • 22
    • 0002449902 scopus 로고
    • Logarithmic structures of Fontaine-Illusie
    • JAMI Conference, Johns Hopkins Univ. Press
    • K. Kato, Logarithmic structures of Fontaine-Illusie, In: Algebraic Analysis, Geometry and Number Theory, JAMI Conference, Johns Hopkins Univ. Press, 1989, pp. 191-224.
    • (1989) Algebraic Analysis, Geometry and Number Theory , pp. 191-224
    • Kato, K.1
  • 23
    • 0347132496 scopus 로고    scopus 로고
    • A letter to K. Kajiwara (in Japanese)
    • K. Kato, Log algebraization, A letter to K. Kajiwara (in Japanese).
    • Log Algebraization
    • Kato, K.1
  • 24
    • 0000040657 scopus 로고
    • Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties
    • Y. Kawamata and Y. Namikawa, Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties, Invent. Math. 118 (1994), 395-409.
    • (1994) Invent. Math. , vol.118 , pp. 395-409
    • Kawamata, Y.1    Namikawa, Y.2
  • 25
    • 0001953616 scopus 로고
    • p-adic variation of the zeta function over families of varieties defined over finite fields
    • N. Koblitz, p-adic variation of the zeta function over families of varieties defined over finite fields, Comp. Math. 31 (1975), 119-218.
    • (1975) Comp. Math. , vol.31 , pp. 119-218
    • Koblitz, N.1
  • 26
    • 0346287282 scopus 로고
    • Degenerations of K3 surfaces and Enriques' surfaces
    • V. Kulikov, Degenerations of K3 surfaces and Enriques' surfaces, Math. USSR Izv. 11 (1977), 957-989.
    • (1977) Math. USSR Izv. , vol.11 , pp. 957-989
    • Kulikov, V.1
  • 27
    • 0002347086 scopus 로고
    • Algebraic solutions of differential equations, p-curvature and the Hodge filtration
    • N. Katz, Algebraic solutions of differential equations, p-curvature and the Hodge filtration, Invent. Math. 18 (1972), 1-118.
    • (1972) Invent. Math. , vol.18 , pp. 1-118
    • Katz, N.1
  • 28
    • 0000001894 scopus 로고
    • Appendix to expose V. Appendix to Cristaux ordinaire et coordonnées canoniques by P. Deligne and L. Illusie
    • Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Springer-Verlag, New York
    • N. Katz, Appendix to expose V. Appendix to Cristaux ordinaire et coordonnées canoniques by P. Deligne and L. Illusie. In: Surfaces algébriques, Séminaire de Géométrie algébrique d'Orsay 1976-1978. Lecture Notes in Math. 868, Springer-Verlag, New York, 1981, pp. 128-137.
    • (1981) Lecture Notes in Math. , vol.868 , pp. 128-137
    • Katz, N.1
  • 29
    • 0002408192 scopus 로고
    • Formal moduli for one-parameter formal Lie groups
    • J. Lubin and J. Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France 94 (1966), 49-60.
    • (1966) Bull. Soc. Math. France , vol.94 , pp. 49-60
    • Lubin, J.1    Tate, J.2
  • 31
    • 0003256969 scopus 로고
    • The crystals associated to Barsotti-Tate groups, with application to abelian schemes
    • Springer-Verlag, New York
    • W. Messing, The crystals associated to Barsotti-Tate groups, with application to abelian schemes, Lecture Notes in Math. 264, Springer-Verlag, New York, 1972.
    • (1972) Lecture Notes in Math. , vol.264
    • Messing, W.1
  • 32
    • 21744434333 scopus 로고    scopus 로고
    • A theory of ordinary p-adic curves
    • Kyoto. Univ.
    • S. Mochizuki, A theory of ordinary p-adic curves, Publ. RIMS. Kyoto. Univ. 32 (1996), 957-1151.
    • (1996) Publ. RIMS , vol.32 , pp. 957-1151
    • Mochizuki, S.1
  • 33
    • 84972488034 scopus 로고
    • On self-intersection number of a section on a ruled surface
    • M. Nagata, On self-intersection number of a section on a ruled surface, Nagoya Math. J. 37 (1970), 191-196.
    • (1970) Nagoya Math. J. , vol.37 , pp. 191-196
    • Nagata, M.1
  • 35
    • 0043097577 scopus 로고
    • The Tate conjecture for ordinary K3 surfaces over finite fields
    • N. O. Nygaard, The Tate conjecture for ordinary K3 surfaces over finite fields, Invent. Math. 74 (1983), 213-237.
    • (1983) Invent. Math. , vol.74 , pp. 213-237
    • Nygaard, N.O.1
  • 36
    • 0000584984 scopus 로고
    • Tate's conjecture for K3 surfaces of finite height
    • N. O. Nygaard and A. Ogus, Tate's conjecture for K3 surfaces of finite height, Ann. of Math. 122 (1985), 461-507.
    • (1985) Ann. of Math. , vol.122 , pp. 461-507
    • Nygaard, N.O.1    Ogus, A.2
  • 38
    • 0346502085 scopus 로고
    • Supersingular K3 crystals
    • Journée de Géométrie algébrique, Rennes 1978
    • A. Ogus, Supersingular K3 crystals, In: Journée de Géométrie algébrique, Rennes 1978, Astérisque 64 (1979), 3-86.
    • (1979) Astérisque , vol.64 , pp. 3-86
    • Ogus, A.1
  • 39
    • 0003265012 scopus 로고
    • F-Crystals, Griffiths transversality, and the Hodge decomposition
    • A. Ogus, F-Crystals, Griffiths transversality, and the Hodge decomposition, Astérisque 221 (1994).
    • (1994) Astérisque , vol.221
    • Ogus, A.1
  • 40
    • 0040487982 scopus 로고
    • Inseparable morphism of algebraic surfaces
    • A. Rudakov and I. Shafarevich, Inseparable morphism of algebraic surfaces, Izv. Akad. Nauk. SSSR Ser. Mat. 40 (1976), No. 6, 1205-1237.
    • (1976) Izv. Akad. Nauk. SSSR Ser. Mat. , vol.40 , Issue.6 , pp. 1205-1237
    • Rudakov, A.1    Shafarevich, I.2
  • 41
    • 0346502079 scopus 로고
    • The influence of height on degeneration of algebraic surfaces of type K3
    • A. Rudakov, T. Zink, and I. Shafarevich, The influence of height on degeneration of algebraic surfaces of type K3, Math. USSR Izv. 20 (1983), 119-135.
    • (1983) Math. USSR Izv. , vol.20 , pp. 119-135
    • Rudakov, A.1    Zink, T.2    Shafarevich, I.3
  • 43
    • 0002642642 scopus 로고
    • Sur la topologie des variétés algébriques en characteristique p
    • Mexico
    • J.-P. Serre, Sur la topologie des variétés algébriques en characteristique p, Symposium Internacional de topologia algebrica, Mexico (1958), 24-53.
    • (1958) Symposium Internacional de Topologia Algebrica , pp. 24-53
    • Serre, J.-P.1
  • 44
    • 0003196712 scopus 로고
    • Revêtements étales et Groupe Fondamentals
    • Springer-Verlag, New York
    • A. Grothendieck et M. Raynaud, Revêtements étales et Groupe Fondamentals, Lecture Notes in Math. 224, Springer-Verlag, New York, 1971.
    • (1971) Lecture Notes in Math. , vol.224
    • Grothendieck, A.1    Raynaud, M.2
  • 45
    • 0002717932 scopus 로고
    • Théorie des Topos et Cohomologie Etale des Schémas
    • Springer-Verlag, New York
    • M. Artin, A. Grothendieck, et J. L. Verdier, Théorie des Topos et Cohomologie Etale des Schémas, Lecture Notes in Math. 305, Springer-Verlag, New York, 1973.
    • (1973) Lecture Notes in Math. , vol.305
    • Artin, M.1    Grothendieck, A.2    Verdier, J.L.3
  • 46
    • 0003235281 scopus 로고
    • Théorie des Intersections et Théorème de Riemann-Roch
    • Springer-Verlag, New York
    • P. Berthelot, A. Grothendieck, et L. Illusie, Théorie des Intersections et Théorème de Riemann-Roch, Lecture Notes in Math. 225, Springer-Verlag, New York, 1971.
    • (1971) Lecture Notes in Math. , vol.225
    • Berthelot, P.1    Grothendieck, A.2    Illusie, L.3
  • 47
    • 0001206359 scopus 로고
    • Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures
    • J. Steenbrink, Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures, Math. Ann. 301 (1995), 105-118.
    • (1995) Math. Ann. , vol.301 , pp. 105-118
    • Steenbrink, J.1
  • 48
    • 0009141124 scopus 로고
    • Formal group laws arising from algebraic varieties
    • J. Stienstra, Formal group laws arising from algebraic varieties, Amer. Jour. of Math. 109 (1987), 907-925.
    • (1987) Amer. Jour. of Math. , vol.109 , pp. 907-925
    • Stienstra, J.1
  • 49
    • 85015172581 scopus 로고    scopus 로고
    • Syntomic complexes and p-adic vanishing cycles
    • T. Tsuji, Syntomic complexes and p-adic vanishing cycles, J. reine angew. Math. 472 (1996), 69-138.
    • (1996) J. Reine Angew. Math. , vol.472 , pp. 69-138
    • Tsuji, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.