Summary
We consider a 1-dimensional differential module (U, ∇) over an algebraic variety X. We assume the singularities of (U, ∇) at infinity to be separated and possibly irregular. We prove that the algebraic de Rham cohomology of X with coefficients in (U, ∇) can be calculated byP-adic analytic methods.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Baldassarri, Comparison entre la cohomologie algébrique et la cohomologieP-adique rigide ä coefficients dans un module differentiel, Inv. Math.,87 (1987), pp. 83–99.
F.Baldassarri, Comparison entre la cohomologie algébrique et la cohomologieP-adique rigide ä coefficients dans un module differentiel-II, to appear in Math. Ann.
F. Baldassarri, Differential modules and singular points ofP-adic differentiel equations, Advances in Math.,44 (1982), pp. 155–179.
R. Berger -R. Kiehl -E. Kunz -H. J. Nastold,Differentialrechnung in der analytischen Geometrie, Lectures Notes in Math.,38, Springer, Berlin-Heidelberg-New York (1967).
S. Bosch -U. Guntzer -R. Remmert,Non archimedean analysis, Wissenschaften,261, Springer, Berlin-Heidelberg-New York-Tokyo (1984).
H. Charriere -R. Gerard,Réduction formelle de certaines connexions linéaires singulières à plusieurs variables, C. R. Acad. Sc. Paris,291 (1980), pp. 391–393 (see also Analysis,1 (1981), pp. 85–115).
B.Chiarellotto, Tesi di Laurea, Padova (1985).
D. Clark, A note on theP-adic convergence of solution of linear differential equations, Proc. Amer. Math. Soc.,17 (1966), pp. 262–269.
P. Deligne,Equations différentielles à points singuliers réguliers, Lectures Notes in Math., Springer, Berlin-Heidelberg-New York (1970).
N. Katz,Nilpotent connections and the monodromy theorem: applications of a result of Turittin, Publ. Math. I.H.E.S.,39 (1970), pp. 355–432.
R. Kiehl,Die de Rham Kohomologie algebraischer Mannigfaltigkeiten über einem bewerteten Korpen, Publ. Math. I.H.E.S.,33 (1967), pp. 5–20.
A. H. M.Levelt - A. R. P.Van Der Essen,Irregular singularities in several variables, Memoirs of Amer. Math. Soc, vol.40, number 270 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chiarellotto, B. A comparison theorem in 115-01115-01115-01-adic cohomology. Annali di Matematica pura ed applicata 153, 115–131 (1988). https://doi.org/10.1007/BF01762389
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01762389