Parity in Bloch’s conductor formula in even dimension

Takeshi Saito[1]

  • [1] Department of Mathematical Sciences, University of Tokyo Tokyo 153-8914 Japan

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 2, page 403-421
  • ISSN: 1246-7405

Abstract

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For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of ℓ -adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.

How to cite

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Saito, Takeshi. "Parity in Bloch’s conductor formula in even dimension." Journal de Théorie des Nombres de Bordeaux 16.2 (2004): 403-421. <http://eudml.org/doc/249274>.

@article{Saito2004,
abstract = {For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of $\ell $-adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.},
affiliation = {Department of Mathematical Sciences, University of Tokyo Tokyo 153-8914 Japan},
author = {Saito, Takeshi},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {2},
pages = {403-421},
publisher = {Université Bordeaux 1},
title = {Parity in Bloch’s conductor formula in even dimension},
url = {http://eudml.org/doc/249274},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Saito, Takeshi
TI - Parity in Bloch’s conductor formula in even dimension
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 2
SP - 403
EP - 421
AB - For a variety over a local field, Bloch proposed a conjectural formula for the alternating sum of Artin conductor of $\ell $-adic cohomology. We prove that the formula is valid modulo 2 if the variety has even dimension.
LA - eng
UR - http://eudml.org/doc/249274
ER -

References

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  7. L. Illusie, Complexe cotangent et déformations I. Lecture notes in Math. 239 Springer. Zbl0224.13014MR491680
  8. K. Kato, T. Saito, Conductor formula of Bloch. To appear in Publ. Math. IHES. Zbl1099.14009MR2102698
  9. T. Ochiai, ℓ -independence of the trace of monodromy. Math. Ann. 315 (1999), 321–340. Zbl0980.14014MR1715253
  10. T. Saito, Self-intersection 0-cycles and coherent sheaves on arithmetic schemes. Duke Math. J. 57 (1988), 555–578. Zbl0687.14004MR962520
  11. —–, Jacobi sum Hecke characters, de Rham discriminant, and the determinant of ℓ -adic cohomologies. J. of Alg. Geom. 3 (1994), 411–434. Zbl0833.14011
  12. J.-P. Serre, Conducteurs d’Artin des caracteres réels. Inventiones Math. 14 (1971), 173–183. Zbl0229.13006MR321908

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