Generic Zariski surfaces

Jeffrey Lang

Compositio Mathematica (1990)

  • Volume: 73, Issue: 3, page 345-361
  • ISSN: 0010-437X

How to cite


Lang, Jeffrey. "Generic Zariski surfaces." Compositio Mathematica 73.3 (1990): 345-361. <>.

author = {Lang, Jeffrey},
journal = {Compositio Mathematica},
keywords = {characteristic p; Zariski surface; divisor class group of the coordinate ring; fundamental group; Zariski open set purely inseparable descent},
language = {eng},
number = {3},
pages = {345-361},
publisher = {Kluwer Academic Publishers},
title = {Generic Zariski surfaces},
url = {},
volume = {73},
year = {1990},

AU - Lang, Jeffrey
TI - Generic Zariski surfaces
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 73
IS - 3
SP - 345
EP - 361
LA - eng
KW - characteristic p; Zariski surface; divisor class group of the coordinate ring; fundamental group; Zariski open set purely inseparable descent
UR -
ER -


  1. 1 P. Blass, Picard groups of Zariski surfaces. I. Comp. Math.54 (1985) 3-86. Zbl0624.14021MR782383
  2. 2 P. Blass and J. Lang, Zariski Surfaces and Differential Equations in Characteristic p &gt; 0. Monographs and Textbooks in Pure and Applied Mathematics, No. 106, Marcel Decker, New York (1987). Zbl0614.14011MR879599
  3. 3 P. Blass and J. Lang, A method for computing the kernel of a map of divisor classes of local rings in characteristic p ≠ 0, Mich. Math. J.35 (1988). Zbl0655.13023MR931940
  4. 4 P. Blass and J. Lang, Surfaces de Zariski factorielles, C. R. Acad. Sc. Paris, T. 306, Série I, (1988). Zbl0671.14025MR944408
  5. 5 P. Deligne and N. Katz, Groupes de Monodromie en Geometrie Algébrique, Lecture Notes in Mathematics340, Springer-Verlag, 1973. Zbl0258.00005MR354657
  6. 6 A. Grant and J. Lang, Applications of the fundamental group and purely inseparable descent to the study of curves on Zariski surfaces, to appear in the Journal of Algebra. Zbl0738.14021
  7. 7 A. Grothendieck, SGAI, Lecture Notes in Mathematics, No. 224, Springer-Verlag, New York, 1971. Zbl0234.14002MR354651
  8. 8 R. Hartshorne, Equivalence relations on algebraic cycles and subvarieties of small codimension, Proc. Symp. Pure Math., 29 (Arcata), American Mathematical Society (1975). Zbl0314.14001MR369359
  9. 9 R. Hartshorne, Algebraic Geometry. Springer-Verlag, New York (1977). Zbl0367.14001MR463157
  10. 10 J. Lang, The divisor class group of the surface zpm = G(x, y) over fields of characteristic p &gt; 0. J. Alg.84, 2 (1983). Zbl0528.14017MR723398
  11. 11 J. Lang, The factoriality of Zarisksi rings. Compositio Mathematica (1987). Zbl0631.13017MR909383
  12. 12 W.E. Lang, Remarks on p-torsion of algebraic surfaces, Compositio Math., 52 (2), (1984) 197-202. Zbl0583.14012MR750355
  13. 13 M. Nagata, Local Rings. John Wiley & Sons, Inc. (1962). Zbl0123.03402MR155856
  14. 14 M. Nagata, Field Theory. Marcel Dekker, Inc. (1977). Zbl0366.12001MR469887
  15. 15 M. Raynaud, Anneaux Locaux Henséliens, Lecture Notes in Mathematics, Springer-Verlag, 1970. Zbl0203.05102MR277519
  16. 16 P. Samuel, Lectures on Unique Factorization Domains. Tata Lecture Notes (1964). Zbl0184.06601MR214579
  17. 17 O. Zariski and P. Samuel, Commutative Algebra, D. Van Nostrand Co., Inc. (1960). Zbl0121.27801MR120249

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.