Quasi-elliptic surfaces in characteristic three

William E. Lang

Annales scientifiques de l'École Normale Supérieure (1979)

  • Volume: 12, Issue: 4, page 473-500
  • ISSN: 0012-9593

How to cite

top

Lang, William E.. "Quasi-elliptic surfaces in characteristic three." Annales scientifiques de l'École Normale Supérieure 12.4 (1979): 473-500. <http://eudml.org/doc/82042>.

@article{Lang1979,
author = {Lang, William E.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Jacobian quasi-elliptic surfaces; characteristic three; crystalline cohomology; de Rham cohomology; Jacobian quasi-hyperelliptic surface; counterexample to Kodaira vanishing theorem; counterexample to Castelnuovo-de Franchis theorem; non-rational Zariski surface},
language = {eng},
number = {4},
pages = {473-500},
publisher = {Elsevier},
title = {Quasi-elliptic surfaces in characteristic three},
url = {http://eudml.org/doc/82042},
volume = {12},
year = {1979},
}

TY - JOUR
AU - Lang, William E.
TI - Quasi-elliptic surfaces in characteristic three
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1979
PB - Elsevier
VL - 12
IS - 4
SP - 473
EP - 500
LA - eng
KW - Jacobian quasi-elliptic surfaces; characteristic three; crystalline cohomology; de Rham cohomology; Jacobian quasi-hyperelliptic surface; counterexample to Kodaira vanishing theorem; counterexample to Castelnuovo-de Franchis theorem; non-rational Zariski surface
UR - http://eudml.org/doc/82042
ER -

References

top
  1. [1] M. ARTIN, Grothendieck Topologies (Lecture Notes, Harvard University, 1962). Zbl0208.48701
  2. [2] P. BLASS, Zariski Surfaces (Thesis, University of Michigan, 1977). 
  3. [3] E. BOMBIERI and D. MUMFORD, Enriques Classification of Surfaces in Characteristic p, Part I, by D. MUMFORD, in Global Analysis, Princeton University Press, 1969 ; Part II, in Complex Analysis and Algebraic Geometry, Cambridge University Press, 1977 ; Part III, Inventiones Math., Vol. 35, 1976. Zbl0336.14010
  4. [4] E. BOMBIERI, Canonical Models of Surfaces of General Type (Publ. Math. I.H.E.S., Vol. 42, 1973). Zbl0259.14005MR47 #6710
  5. [5] P. DELIGNE, Courbes elliptiques, formulaire, d'après J. Tate, in Modular Functions of One Variable IV (Springer Lecture Notes in Math., No. 476, 1975). MR52 #8135
  6. [6] I. DOLGACEV, The Euler Characteristic of a Family of Algebraic Varieties (Math. U.S.S.R. Sbornik, Vol. 18, 1972). Zbl0263.14002MR48 #6116
  7. [7] R. HARTSHORNE, Algebraic Geometry, Springer Verlag, 1977. Zbl0367.14001MR57 #3116
  8. [8] S. IITAKA, Deformations of Compact Complex Surfaces, in Global Analysis, Princeton University Press, 1969. Zbl0188.53305MR40 #8086
  9. [9] L. ILLUSIE, Report on Crystalline Cohomology, in Proceedings of Symposium in Pure Math., Vol. 29, American Mathematical Society, 1975. Zbl0326.14005MR52 #13845
  10. [10] L. ILLUSIE, Complexe de De Rham-Witt et Cohomologie Cristalline (Ann. scient. Éc. Norm. Sup., T. 12, 1979, pp. 509-669). Zbl0436.14007MR82d:14013
  11. [11] S. T. JENSEN, Picard Schemes of Quotients by Finite Commutative Group Schemes (Math. Scand., Vol. 42, 1978). Zbl0406.14027MR80a:14015
  12. [12] K. KODAIRA, On Compact Analytic Surfaces II (Ann. of Math., Vol. 77, 1963). Zbl0118.15802
  13. [13] W. E. LANG, Quasi-Elliptic Surfaces in Characteristic Three (Thesis, Harvard University, 1978). 
  14. [14] W. E. LANG, Two Theorems on de Rham Cohomology (preprint). Zbl0508.14011
  15. [15] M. MIYANISHI, Unirational Quasi-Elliptic Surfaces in Characteristic 3 (Osaka J. Math., Vol. 13, 1976). Zbl0358.14019MR55 #10471
  16. [16] D. MUMFORD, Pathologies of Modular Algebraic Surfaces (Amer. J. Math., Vol. 83, 1961). Zbl0138.42002MR23 #A1642
  17. [17] D. MUMFORD, Lectures on Curves on an Algebraic Surface (Ann. of Math. Studies, Vol. 59, Princeton, 1966). Zbl0187.42701MR35 #187
  18. [18] D. MUMFORD, Abelian Varieties, Tata Studies in Math., Oxford University Press, 1970. Zbl0223.14022MR44 #219
  19. [19] D. MUMFORD and K. SUOMINEN, Introduction to the Theory of Moduli, in Algebraic Geometry, Oslo, 1970. Zbl0242.14004
  20. [20] D. MUMFORD, Some Footnotes to the Work of C. P. Ramanujam (to appear). Zbl0444.14002
  21. [21] A. NERON, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux (Publ. Math. I.H.E.S., Vol. 21, 1964). Zbl0132.41403MR31 #3423
  22. [22] T. ODA, The First de Rham Cohomology Group and Dieudonne Modules (Ann. scient. Éc. Norm. Sup., T. 2, 1969). Zbl0175.47901MR39 #2775
  23. [23] T. ODA, Vector Bundles on an Elliptic Curve (Nagoya Math. J., Vol. 43, 1971). Zbl0201.53603MR47 #6700
  24. [24] C. QUEEN, Non-conservatrice Function Fields of Genus One, Part I (Arch. Math., Basel, Vol. 22, 1971) ; Part II (Arch. Math., Basel, Vol. 23, 1972). Zbl0251.14011
  25. [25] M. RAYNAUD, Contre-exemple de "vanishing de Kodaira" sur une surface lisse en car. p &gt; 0 (preprint). 
  26. [26] A. RUDAKOV and I. SAFEREVIC, Inseparable Morphisms of Algebraic Surfaces (Math. U.S.S.R. Izvestija, Vol. 10, 1976). Zbl0379.14006
  27. [27] P. RUSSELL, Forms of the Affine Line and its Additive Group (Pac. J. Math., Vol. 32, 1970). Zbl0199.24502MR42 #277
  28. [28] I. SAFEREVIC et al., Algebraic Surfaces (Proc. Steklov Inst. Math., Vol. 75, 1965). 
  29. [29] I. SAFEREVIC, Basic Algebraic Geometry, Springer-Verlag, 1974. 
  30. [30] J.-P. SERRE, Sur la topologie des variétés algébriques en caractéristique p, in Symposium Internacional de Topologia Algebraica, 1958. Zbl0098.13103MR20 #4559
  31. [31] T. SHIODA, Some Results on Unirationality of Algebraic Surfaces (Math. Ann., Vol. 230, 1977). Zbl0343.14021MR58 #28004
  32. [32] T. SUWA, On Hyperelliptic surfaces (J. Fac. Sc., University of Tokyo, Vol. 16, 1969). Zbl0256.14014MR42 #2035
  33. [33] H. TANGO, On the Behavior of Extensions of Vector Bundles Under the Frobenius Map (Nagoya Math., J., Vol. 48, 1972). Zbl0239.14007MR47 #3401
  34. [34] J. TATE, Genus Change in Purely Inseparable Extension of Function Fields (Proc. Amer. Math. Soc., Vol. 3, 1952). Zbl0047.03901MR13,905b
  35. [35] J. TATE, Appendix to Elliptic Functions, by S. LANG, Addison-Wesley, 1973. MR53 #13117
  36. [36] J. TATE, The arithmetic of elliptic curves (Invent. Math., Vol. 23, 1974). Zbl0296.14018MR54 #7380
  37. [37] O. ZARISKI, Collected Papers, Vol. I and II, M.I.T. Press, 1972, 1973. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.