Frobenius and the Hodge filtration. (English) Zbl 0258.14006


14G20 Local ground fields in algebraic geometry
14G15 Finite ground fields in algebraic geometry
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14F30 \(p\)-adic cohomology, crystalline cohomology
Full Text: DOI


[1] J. Berthelot, A series of notes in the C. R. Acad. Sci. Paris Sér. A-B 269 (1969), A297-A300; A357-A360; A397-A400; ibid. 272 (1971), A141-A144; A1314-A1317; A1397-A1400. MR 40 #151; #2686;41 #8432.
[2] Bernard Dwork, A deformation theory for the zeta function of a hypersurface, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 247 – 259.
[3] N. Katz, A note on a theorem of Ax, Mimeographed Notes, Princeton University, Princeton, N.J., 1970.
[4] Nicholas M. Katz, On the differential equations satisfied by period matrices, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 223 – 258.
[5] N. Katz, Seminar on degeneration of algebraic varieties, Inst. for Advanced Study, Princeton, N.J., Mimeographed Notes, Fall Term, 1969/70.
[6] S. Kleiman, Weil cohomologies, Dix exposés sur la théorie des schémas, NorthHolland, Amsterdam.
[7] Ju. I. Manin, The Hasse-Witt matrix of an algebraic curve, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 153 – 172 (Russian). · Zbl 0102.27802
[8] B. Mazur, Frobenius and the Hodge filtration (estimates), Ann. of Math. (2) 98 (1973), 58 – 95. · Zbl 0261.14005
[9] Leonhard Miller, Curves with invertible Hasse-Witt-matrix, Math. Ann. 197 (1972), 123 – 127. · Zbl 0235.14009
[10] David Mumford, Bi-extensions of formal groups, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969, pp. 307 – 322.
[11] E. Warning, Bemerkung zur vorstehenden Arbeit von Herr Chevalley, Abh. Math. Sem. Univ. Hamburg 11 (1936), 76-83. · JFM 61.1043.02
[12] André Weil, Jacobi sums as ”Grössencharaktere”, Trans. Amer. Math. Soc. 73 (1952), 487 – 495. · Zbl 0048.27001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.