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Index of a \(p\)-adic linear differential operator of first order and \(p\)-adic cohomology. (Indice d’un opérateur différentiel linéaire \(p\)-adique d’ordre 1 et cohomologie \(p\)-adique.) (French) Zbl 0517.12013
Groupe Étude Anal. Ultramétrique 9e Année: 1981/82, No. 3, No. J15, 10 pp. (1983).
Translated from the French summary: Motivated by the recent work of B. Dwork [Am. J. Math. 105, 115–156 (1983; Zbl 0517.12012)], A. Adolphson and S. Sperber [Am. J. Math. 106, 549–591 (1984; Zbl 0552.12010)] on \(p\)-adic cohomologies associated with mixed exponential sums, I will give in this exposé a systematic study of analytic \(p\)-adic cohomology in one variable.
All proofs and a detailed bibliography will appear in a forthcoming paper [“Index of \(p\)-adic differential operators. I–III,” (I) Ann. Math. (2) 101, 280–316 (1975; Zbl 0316.12102), (II) Duke Math. J. 43, 19–31 (1976; Zbl 0338.12108), (III) Cohomologie \(p\)-adique, Astérisque 119–120, 191–266 (1984; Zbl 0548.12015)].

MSC:
12H25 \(p\)-adic differential equations
14F30 \(p\)-adic cohomology, crystalline cohomology
Full Text: Numdam