Supersingular K 3 surfaces

M. Artin

Annales scientifiques de l'École Normale Supérieure (1974)

  • Volume: 7, Issue: 4, page 543-567
  • ISSN: 0012-9593

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Artin, M.. "Supersingular $K3$ surfaces." Annales scientifiques de l'École Normale Supérieure 7.4 (1974): 543-567. <http://eudml.org/doc/81948>.

@article{Artin1974,
author = {Artin, M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {4},
pages = {543-567},
publisher = {Elsevier},
title = {Supersingular $K3$ surfaces},
url = {http://eudml.org/doc/81948},
volume = {7},
year = {1974},
}

TY - JOUR
AU - Artin, M.
TI - Supersingular $K3$ surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1974
PB - Elsevier
VL - 7
IS - 4
SP - 543
EP - 567
LA - eng
UR - http://eudml.org/doc/81948
ER -

References

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  1. [1] M. ARTIN, Algebraic approximation of structures over complete local rings (Pub. Math. Inst. Hautes Études Sci., vol. 36, 1969, p. 23-58). Zbl0181.48802MR42 #3087
  2. [2] M. ARTIN, Algebraic construction of Brieskorn's resolutions (J. Alg., vol. 29, 1974, p. 330-348). Zbl0292.14013MR50 #7143
  3. [3] M. ARTIN, A. GROTHENDIECK and J.-L. VERDIER, Théorie des topos et cohomologie des schémas, T. 3 (Lecture Notes in Mathematics, No. 305, Springer, Berlin, 1973). Zbl0245.00002MR50 #7132
  4. [4] M. ARTIN and B. MAZUR, Formal groups arising from algebraic varieties (to appear). Zbl0351.14023
  5. [5] M. ARTIN and H. P. F. SWINNERTON-DYER, The Shafarevich-Tate conjecture for pencils of elliptic curves on K 3 surfaces (Invent. Math., vol. 20, 1973, p. 249-266). Zbl0289.14003MR54 #5240
  6. [6] A. GROTHENDIECK, Éléments de géométrie algébrique III, (Pub. Math. Inst. Hautes Études Sci., vol. 11, 1961). Zbl0235.14007
  7. [7] A. GROTHENDIECK, Le groupe de Brauer (Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968). Zbl0192.57801
  8. [8] J.-I. IGUSA, Betti and Picard numbers of abstract algebraic surfaces (Proc. Nat. Acad. Sci., vol. 46, 1960, p. 724-726). Zbl0099.16402MR22 #9496
  9. [9] K. KODAIRA, On compact analytic surfaces II (Ann. of Math., vol. 77, 1963, p. 563-626). Zbl0118.15802
  10. [10] M. LAZARD, Sur les groupes de Lie formels à un paramètre (Bull. Soc. math. Fr., vol. 83, 1955, p. 251-274). Zbl0068.25703MR17,508e
  11. [11] F. OORTCommutative group schemes (Lecture Notes in Mathematics, No. 15, Springer, Berlin, 1966. Zbl0216.05603MR35 #4229
  12. [12] PIATETSKI-SHAPIRO and I. R. SHAFAREVICH, A Torelli theorem for algebraic surfaces of type K 3 (Izv. Akad. Nauk. S.S.S.R., vol. 35, 1971, and Math. U.R.S.S. (Izvestia, vol. 5, 1971, p. 547-588). Zbl0253.14006
  13. [13] M. RAYNAUD, Caractéristique d'Euler-Poincaré d'un faisceau et cohomologie des variétés abéliennes (Séminaire Bourbaki 1964-1965. Exposé, reprinted in Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968). Zbl0204.54301
  14. [14] J.-P. SERRE, Groupes pro-algébriques (Pub. Math. Inst. Hautes Études Sci., vol. 7, 1960). MR22 #9493
  15. [15] J.-P. SERRE, Cours d'arithmétique, Presses Universitaires de France, Paris, 1970. Zbl0225.12002MR41 #138
  16. [16] T. SHIODA, On elliptic modular surfaces (J. Math. Soc. Japan, vol. 24, 1972, p. 20-59). Zbl0226.14013MR55 #2927
  17. [17] T. SHIODA, On rational points of the generic elliptic curve with level N structure over the field of mudular functions of level N (J. Math. Soc. Japan, vol. 25, 1973, p. 144-157). Zbl0243.14009MR47 #5001
  18. [18] T. SHIODA, Algebraic cycles on certain K 3 surfaces in characteristic p (to appear). Zbl0311.14007
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  20. [20] J. TATE, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog (Séminaire Bourbaki, 1965/1966. Exposé 306, reprinted in Dix exposés sur la cohomologie des schémas, North Holland, Amsterdam, 1968). Zbl0199.55604

Citations in EuDML Documents

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  1. Matthias Schütt, Andreas Schweizer, On the uniqueness of elliptic K3 surfaces with maximal singular fibre
  2. Niels O. Nygaard, Slopes of powers of Frobenius on crystalline cohomology
  3. Spencer Bloch, Algebraic K -theory and crystalline cohomology
  4. Niels O. Nygaard, Higher de Rham-Witt complexes of supersingular K3 surfaces
  5. Florent Jouve, The geometry of the third moment of exponential sums
  6. J. S. Milne, Duality in the flat cohomology of a surface
  7. Fedor Bogomolov, Yuri Zarhin, Ordinary reduction of K3 surfaces
  8. M. Artin, B. Mazur, Formal groups arising from algebraic varieties
  9. W. J. Gordon, Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer
  10. Luc Illusie, Complexe de de Rham-Witt et cohomologie cristalline

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