Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-26T12:20:08.463Z Has data issue: false hasContentIssue false
  • English
  • Français

On twisted de Rham cohomology

Published online by Cambridge University Press:  22 January 2016

Alan Adolphson  and
Steven Sperber
Alan Adolphson
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, adolphs@.math.okstate.edu
Steven Sperber
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, sperber@vx.cis.umn.edu
Rights & Permissions [Opens in a new window]

Abstract.

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider the complex of differential forms on an open affine subvariety U of AN with differential where d is the usual exterior derivative and ø is a fixed 1-form on U. For certain U and ø, we compute the cohomology of this complex.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 146 , June 1997 , pp. 55 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[A] Adolphson, A., Hypergeometric functions and rings generated by monomials, Duke Math. J., 73 (1994), 269–290.CrossRefGoogle Scholar
[AS1] Adolphson, A. and Sperber, S., Newton polyhedra and the degree of the L-function associated to an exponential sum. Invent. Math., 88 (1987), 555–569.CrossRefGoogle Scholar
[AS2] Adolphson, A. and Sperber, S., On the degree of the L-function associated with an exponential sum, Comp. Math., 68 (1988), 125–159.Google Scholar
[AS3] Adolphson, A. and Sperber, S., Exponential sums and Newton polyhedra: Cohomology and estimates, Ann. of Math., 130 (1989), 367–406.Google Scholar
[AS4] Adolphson, A. and Sperber, S., Twisted exponential sums and Newton polyhedra, J. reine und angew. Math., 443 (1993), 151–177.Google Scholar
[AS5] Adolphson, A. and Sperber, S., On the zeta function of a complete intersection, Ann. Sci. E. N. S. (to appear).Google Scholar
[AKOT] Aomoto, K., Kita, M., Orlik, P., and Terao, H., Twisted de Rham cohomology groups of logarithmic forms (preprint).Google Scholar
[B] Batyrev, V. V., Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori, Duke Math. J., 69 (1993), 349–409.Google Scholar
[DW1] Dwork, B., On the zeta function of a hypersurface, Publ. Math. I. H. E. S., 12 (1962), 5–68.CrossRefGoogle Scholar
[DW2] Dwork, B., Generalized Hypergeometric Functions, Oxford Mathematical Monographs, Clarendon, New York, 1990.Google Scholar
[DL] Dwork, B. and Loeser, F., Hypergeometric series, Japan. J. Math., 19 (1993), 81–129.CrossRefGoogle Scholar
[GKZ] Gelfand, I. M., Kapranov, M. M., and Zelevinsky, A. V., Generalized Euler integrals and A-hypergeometric functions, Adv. Math., 84 (1990), 255–271.CrossRefGoogle Scholar
[H] Hochster, M., Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and poly topes, Ann. of Math., 96 (1972), 318–337.Google Scholar
[K1] Katz, N., Thesis (1966), Princeton University.Google Scholar
[K2] Katz, N., On the differential equations satisfied by period matrices, Publ. Math. I. H. E. S., 35 (1968), 223–258.CrossRefGoogle Scholar
[KI] Kita, M., On vanishing of the twisted rational de Rham cohomology associated with hypergeometric functions, Nagoya Math. J., 135 (1994), 55–85.CrossRefGoogle Scholar
[KO] Kouchnirenko, A. G., Polyèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1–31.CrossRefGoogle Scholar
[M] Matsumura, H., Commutative Ring Theory, Cambridge University Press, Cambridge, 1986.Google Scholar