Internal reconstruction of unit-root F -crystals via expansion-coefficients. With an appendix by Luc Illusie

Nicholas M. Katz

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 2, page 245-285
  • ISSN: 0012-9593

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Katz, Nicholas M.. "Internal reconstruction of unit-root $F$-crystals via expansion-coefficients. With an appendix by Luc Illusie." Annales scientifiques de l'École Normale Supérieure 18.2 (1985): 245-285. <http://eudml.org/doc/82159>.

@article{Katz1985,
author = {Katz, Nicholas M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {expansion coefficients; Witt vectors; Hodge-Witt decompositions; de Rham cohomology; transversality; unit-root F-crystal; Hasse-Witt operation; Cartier operator},
language = {eng},
number = {2},
pages = {245-285},
publisher = {Elsevier},
title = {Internal reconstruction of unit-root $F$-crystals via expansion-coefficients. With an appendix by Luc Illusie},
url = {http://eudml.org/doc/82159},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Katz, Nicholas M.
TI - Internal reconstruction of unit-root $F$-crystals via expansion-coefficients. With an appendix by Luc Illusie
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 2
SP - 245
EP - 285
LA - eng
KW - expansion coefficients; Witt vectors; Hodge-Witt decompositions; de Rham cohomology; transversality; unit-root F-crystal; Hasse-Witt operation; Cartier operator
UR - http://eudml.org/doc/82159
ER -

References

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  3. [Cib] P. R. CIBOTTO, Congruences for Abelian Integrals (Boll. U.M.I., (15), Vol. 18-A, 1981, pp. 431-433). Zbl0483.14007MR83h:14034
  4. [Dw-1] B. DWORK, A Deformation Theory for the Zeta Function of a Hypersurface (Proc. Int'l Cong. Math., 1962, pp. 247-259). Zbl0196.53302
  5. [Dw-2] B. DWORK, P-adic Cycles (Publ. Math. I.H.E.S., Vol. 37, 1970, pp. 27-115). Zbl0284.14008MR45 #3415
  6. [Dw-3] B. DWORK, Normalized Period Matrices (Annals of Math., Vol. 94, 1971, pp. 337-388). Zbl0241.14011MR53 #442a
  7. [Ill] L. ILLUSIE, Complexe de de Rham-Witt et Cohomologie crystalline (Ann. scient. Éc. Norm. Sup., 4e série, T. 12, 1979, pp. 501-661). Zbl0436.14007MR82d:14013
  8. [Ill-Ray] L. ILLUSIE, M. RAYNAUD, Les suites spectrales associées au complexe de de Rham-Witt (Pub. Math. I.H.E.S., Vol. 57, 1983, pp. 73-212). Zbl0538.14012MR85e:14026
  9. [Ka-1] N. KATZ, Travaux de Dwork [Séminaire Bourbaki, 1971/1972 (Springer Lecture Notes in Mathematics, No. 317, 1973, pp. 167-200)]. Zbl0259.14007MR58 #16672
  10. [Ka-2] N. KATZ, Slope Filtration of F-Crystals (Astérisque, Vol. 63, 1979, pp. 113-164). Zbl0426.14007MR81i:14014
  11. [Ka-3] N. KATZ, Crystalline Cohomology, Dieudonné Modules and Jacobi Sums, in Automorphic Forms, Representation Theory, and Arithmetic, T.I.F.R., Bombay, January 1979, Springer-Verlag, 1981, pp. 165-246. Zbl0502.14007MR83a:14022
  12. [Ka-4] N. KATZ, Expansion-Coefficients as Approximate Solutions of Differential Equations [Astérisque (to appear)]. 
  13. [Ka-Me] N. KATZ and W. MESSING, Some Consequences of the Riemann Hypothesis for Varieties Over Finite Fields (Inv. Math., Vol. 23, 1974, pp. 73-77). Zbl0275.14011MR48 #11117
  14. [Maz-1] B. MAZUR, Frobenius and the Hodge Filtration (B.A.M.S., Vol. 78, 1972, pp. 653-667). Zbl0258.14006MR48 #8507
  15. [Maz-2] B. MAZUR, Frobenius and the Hodge Filtration-Estimates (Annals of Math., Vol. 88, 1973, pp. 58-95). Zbl0261.14005MR48 #297
  16. [Milne] J. S. MILNE, Duality in the Flat Cohomology of a Surface (Ann. scient. Éc. Norm. Sup., 4e série, T. 9, 1976, pp. 717-202). Zbl0334.14010MR57 #325
  17. [Ek] T. EKEDAHL, Diagonal Complexes and F-Gauge Structures, in preparation. Zbl0593.14016
  18. [Ill 1] L. ILLUSIE, Finiteness, Duality, and Künneth Theorems in the Cohomology of the De Rham-Witt Complex (in Algebraic Geometry, Tokyo/Kyoto, 1982, Springer Lecture Notes in Mathematics, n° 1016, 1983, p. 20-72). Zbl0538.14013
  19. [Ka 5] N. KATZ, Une formule de congruence pour la fonction zêta [SGA 7, Groupes de monodromie en géométrie algébrique, exp. XXII Springer Lecture Notes in Mathematics, n° 340, 1973, p. 401-438). Zbl0275.14015MR50 #7135
  20. [Ka 6] N. KATZ, International Reconstruction of Unit-Root F-Crystals via Expansion-coefficients, this issue. 
  21. [Ny] N. NYGAARD, Slopes of Powers of Frobenius on Crystalline Cohomology (Ann. scient. Éc. Norm. Sup., 4e série, 1981, p. 369-401). Zbl0519.14012MR84d:14011

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