Etale p -covers in characteristic p

Richard M. Crew

Compositio Mathematica (1984)

  • Volume: 52, Issue: 1, page 31-45
  • ISSN: 0010-437X

How to cite


Crew, Richard M.. "Etale $p$-covers in characteristic $p$." Compositio Mathematica 52.1 (1984): 31-45. <>.

author = {Crew, Richard M.},
journal = {Compositio Mathematica},
keywords = {étale -covers; torsionless fundamental group; group acting on scheme; -ranks of smooth projective curves; characteristic ; Euler-Poincaré characteristic; singular Enriques surface},
language = {eng},
number = {1},
pages = {31-45},
publisher = {Martinus Nijhoff Publishers},
title = {Etale $p$-covers in characteristic $p$},
url = {},
volume = {52},
year = {1984},

AU - Crew, Richard M.
TI - Etale $p$-covers in characteristic $p$
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 1
SP - 31
EP - 45
LA - eng
KW - étale -covers; torsionless fundamental group; group acting on scheme; -ranks of smooth projective curves; characteristic ; Euler-Poincaré characteristic; singular Enriques surface
UR -
ER -


  1. [1] M. Artin and D. Mumford: Some elementary examples of unirational varities which are not rational. Proc., London Math. Soc.25, pp. 75-95. Zbl0244.14017MR321934
  2. [2] P. Berthelot: Cohomologie cristalline des Schemas de caracteristique p &gt; 0. Lecture Notes in Math. #407, Springer1974. Zbl0298.14012MR384804
  3. [3] P. Berthelot and A. Ogus: Notes on crystalline cohomology. Mathematical Notes #21, Princeton University Press, 1978. Zbl0383.14010MR491705
  4. [4] E. Bombieri and D. Mumford: Enriques classification of surfaces in char. p. III. Inv. Math.35 (1976) 197-232. Zbl0336.14010MR491720
  5. [5] P. Blass: Unirationality of Enriques surfaces in characteristic two, (to appear). Zbl0549.14019
  6. [6] L. Illusie: Complexe de De Rham-Witt et cohomologie cristalline. Ann. Scient. Ec. Norm. Sup. 4e serie t. 12 (1979) 501-661. Zbl0436.14007MR565469
  7. [7] T. Katsura: Surfaces unirationelles en caracteristique p. C.R. Acad. Sc. Paris, t. 288 series A (1979) 45-47. Zbl0429.14011MR522017
  8. [8] N. Katz: Travaux de Dwork. In: Sem Bourbaki, exp. 409. Lecture Notes in Math. #317, Springer1973. Zbl0259.14007MR498577
  9. [9] N. Nygaard: On the fundamental group of a unirational 3-fold. Inv. Math.44 (1978) 75-86. Zbl0427.14014MR491731
  10. [10] J.-P. Serre: On the fundamental group of a unirational variety. J. London Math. Soc.1(14) (1959) 481-484. Zbl0097.36301MR109155
  11. [11] J.-P. Serre: Representations Lineaires des Groupes Finis, 2nd edn., Paris, Hermann1971. Zbl0223.20003MR352231
  12. [12] I. Shafarevich: On p-extensions. Mat. Sbornik20 (1947) 351-363 (AMS Translations Ser. 2 vol. 4, 1956). Zbl0041.17101MR20546
  13. [13] S. Shatz: Profinite groups, arithmetic, and geometry. Ann. Math. Studies #67, Princeton University Press1972. Zbl0236.12002MR347778
  14. [14] T. Shioda: An example of unirational surfaces in characteristic p. Math. Ann.211 (1974) 233-236. Zbl0276.14018MR374149
  15. [SGA1] A. Grothendieck: Revêtements etales et groupe fondamental. Lecture Notes in Math224, Springer-Verlag1971. Zbl0234.14002MR354651
  16. [SGA4] M. Artin, A. Grothendieck and J.-L. Verdier: Théorie des topos et cohomologie etale des schémas. Lecture Notes in Math. 269, 270, 305, Springer-Verlag1972 -1973. Zbl0245.00002
  17. [SGA41/2] P. Deligne: Cohomologie etale. Lecture Notes in Math. 569, Springer-Verlag1977. Zbl0345.00010MR463174
  18. [SGA5] A. Grothendieck: Cohomologie l-adique et fonctions L. Lecture Notes in Math. 589, Springer-Verlag1977. Zbl0345.00011MR463174
  19. [SGA6] P. Berthelot, A. Grothendieck and L. Illusie: Théorie des intersections et théorème de Riemann-Roch. Lecture Notes in Math. 225, Springer-Verlag1971. Zbl0218.14001MR354655
  20. [SGA7] A. Grothendieck, M. Raynaud, D. Rim, P. Deligne and N. Katz: Groupes de Monodromie en Géométrie Algébrique. Lecture Notes in Math. 288-340, Springer-Verlag1972-1973. 

NotesEmbed ?


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.