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Frobenius and the Hodge filtration. (English) Zbl 0258.14006


MSC:

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
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References:

[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.
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[8] B. Mazur, Frobenius and the Hodge filtration (estimates), Ann. of Math. (2) 98 (1973), 58 – 95. · Zbl 0261.14005 · doi:10.2307/1970906
[9] Leonhard Miller, Curves with invertible Hasse-Witt-matrix, Math. Ann. 197 (1972), 123 – 127. · Zbl 0235.14009 · doi:10.1007/BF01419588
[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
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