Homology for irregular connections

Spencer Bloch[1]; Hélène Esnault[2]

  • [1] Dept. of Mathematics University of Chicago Chicago, IL 60637, USA
  • [2] Mathematik Universität Essen FB6, Mathematik 45117 Essen, Germany

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 2, page 357-371
  • ISSN: 1246-7405

Abstract

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Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.

How to cite

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Bloch, Spencer, and Esnault, Hélène. "Homology for irregular connections." Journal de Théorie des Nombres de Bordeaux 16.2 (2004): 357-371. <http://eudml.org/doc/249277>.

@article{Bloch2004,
abstract = {Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.},
affiliation = {Dept. of Mathematics University of Chicago Chicago, IL 60637, USA; Mathematik Universität Essen FB6, Mathematik 45117 Essen, Germany},
author = {Bloch, Spencer, Esnault, Hélène},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {2},
pages = {357-371},
publisher = {Université Bordeaux 1},
title = {Homology for irregular connections},
url = {http://eudml.org/doc/249277},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Bloch, Spencer
AU - Esnault, Hélène
TI - Homology for irregular connections
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 2
SP - 357
EP - 371
AB - Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.
LA - eng
UR - http://eudml.org/doc/249277
ER -

References

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  2. N. Kachi, K. Matsumoro, M. Mihara, The perfectness of the intersection pairings for twisted cohomology and homology groups with respect to rational 1 -forms. Kyushu J. Math. 53 (1999), 163–188. Zbl0933.14009MR1678026
  3. G. Laumon, Transformation de Fourier, constantes d’équations fonctionnelles, et conjecture de Weil. Publ. Math. IHES 65 (1987), 131–210. Zbl0641.14009MR908218
  4. B. Malgrange, Équations Différentielles à Coefficients Polynomiaux. Progress in Math. 96, Birkhäuser Verlag, 1991. Zbl0764.32001MR1117227
  5. B. Malgrange, Remarques sur les équations différentielles à points singuliers irréguliers. Springer Lecture Notes in Mathematics 712 (1979), 77–86. Zbl0423.32014MR548145
  6. B. Malgrange, Sur les points singuliers des équations différentielles. L’Enseignement mathématique, t. 20, 1-2 (1974), 147–176. Zbl0299.34011MR368074
  7. T. Saito, T. Terasoma, Determinant of Period Integrals. J. AMS 10 (1997), 865–937. Zbl0956.14005MR1444751
  8. T. Terasoma, Confluent Hypergeometric Functions and Wild Ramification. Journ. of Algebra 185 (1996), 1–18. Zbl0873.12004MR1409971
  9. T. Terasoma, A Product Formula for Period Integrals. Math. Ann. 298 (1994), 577–589. Zbl0811.32014MR1268595
  10. G.N. Watson, E.T. Whittaker, A Course of modern Analysis. Cambridge University Press, 1965. Zbl45.0433.02MR1424469

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