Internal reconstruction of unit-root F-crystals via expansion-coefficients. With an appendix by Luc Illusie
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 18 (1985) no. 2, p. 245-285
@article{ASENS_1985_4_18_2_245_0,
     author = {Katz, Nicholas},
     title = {Internal reconstruction of unit-root $F$-crystals via expansion-coefficients. With an appendix by Luc Illusie},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 18},
     number = {2},
     year = {1985},
     pages = {245-285},
     doi = {10.24033/asens.1490},
     zbl = {0592.14021},
     mrnumber = {87a:14019},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1985_4_18_2_245_0}
}
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, Serie 4, Volume 18 (1985) no. 2, pp. 245-285. doi : 10.24033/asens.1490. http://www.numdam.org/item/ASENS_1985_4_18_2_245_0/

[B-O] P. Berthelot and A. Ogus, Notes on Crystalline Cohomology, Princeton University Press, 1978. | MR 58 #10908 | Zbl 0383.14010

[Cart] P. Cartier, Questions de rationalité des diviseurs en géométrie algébrique (Bull. Soc. math. Fr., T. 86, Fasc. III, 1958, pp. 177-251). | Numdam | MR 21 #4957 | Zbl 0091.33501

[Cib] P. R. Cibotto, Congruences for Abelian Integrals (Boll. U.M.I., (15), Vol. 18-A, 1981, pp. 431-433). | MR 83h:14034 | Zbl 0483.14007

[Dw-1] B. Dwork, A Deformation Theory for the Zeta Function of a Hypersurface (Proc. Int'l Cong. Math., 1962, pp. 247-259). | Zbl 0196.53302

[Dw-2] B. Dwork, P-adic Cycles (Publ. Math. I.H.E.S., Vol. 37, 1970, pp. 27-115). | Numdam | MR 45 #3415 | Zbl 0284.14008

[Dw-3] B. Dwork, Normalized Period Matrices (Annals of Math., Vol. 94, 1971, pp. 337-388). | MR 53 #442a | Zbl 0241.14011

[Ill] L. Illusie, Complexe de de Rham-Witt et Cohomologie crystalline (Ann. scient. Éc. Norm. Sup., 4e série, T. 12, 1979, pp. 501-661). | Numdam | MR 82d:14013 | Zbl 0436.14007

[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). | Numdam | MR 85e:14026 | Zbl 0538.14012

[Ka-1] N. Katz, Travaux de Dwork [Séminaire Bourbaki, 1971/1972 (Springer Lecture Notes in Mathematics, No. 317, 1973, pp. 167-200)]. | Numdam | MR 58 #16672 | Zbl 0259.14007

[Ka-2] N. Katz, Slope Filtration of F-Crystals (Astérisque, Vol. 63, 1979, pp. 113-164). | MR 81i:14014 | Zbl 0426.14007

[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. | MR 83a:14022 | Zbl 0502.14007

[Ka-4] N. Katz, Expansion-Coefficients as Approximate Solutions of Differential Equations [Astérisque (to appear)].

[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). | MR 48 #11117 | Zbl 0275.14011

[Maz-1] B. Mazur, Frobenius and the Hodge Filtration (B.A.M.S., Vol. 78, 1972, pp. 653-667). | MR 48 #8507 | Zbl 0258.14006

[Maz-2] B. Mazur, Frobenius and the Hodge Filtration-Estimates (Annals of Math., Vol. 88, 1973, pp. 58-95). | MR 48 #297 | Zbl 0261.14005

[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). | Numdam | MR 57 #325 | Zbl 0334.14010

[Ek] T. Ekedahl, Diagonal Complexes and F-Gauge Structures, in preparation.

[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). | Zbl 0538.14013

[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). | MR 50 #7135 | Zbl 0275.14015

[Ka 6] N. Katz, International Reconstruction of Unit-Root F-Crystals via Expansion-coefficients, this issue.

[Ny] N. Nygaard, Slopes of Powers of Frobenius on Crystalline Cohomology (Ann. scient. Éc. Norm. Sup., 4e série, 1981, p. 369-401). | Numdam | MR 84d:14011 | Zbl 0519.14012