An Arakelov theoretic proof of the equality of conductor and discriminant

Sinan Ünver[1]

  • [1] Department of Mathematics University of Chicago 5734 S. University Ave. Chicago IL 60637, USA

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 2, page 423-427
  • ISSN: 1246-7405

Abstract

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We give an Arakelov theoretic proof of the equality of conductor and discriminant.

How to cite

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Ünver, Sinan. "An Arakelov theoretic proof of the equality of conductor and discriminant." Journal de Théorie des Nombres de Bordeaux 16.2 (2004): 423-427. <http://eudml.org/doc/249267>.

@article{Ünver2004,
abstract = {We give an Arakelov theoretic proof of the equality of conductor and discriminant.},
affiliation = {Department of Mathematics University of Chicago 5734 S. University Ave. Chicago IL 60637, USA},
author = {Ünver, Sinan},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Arakelov geometry; conductor and discriminant; arithmetic Noether's formula},
language = {eng},
number = {2},
pages = {423-427},
publisher = {Université Bordeaux 1},
title = {An Arakelov theoretic proof of the equality of conductor and discriminant},
url = {http://eudml.org/doc/249267},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Ünver, Sinan
TI - An Arakelov theoretic proof of the equality of conductor and discriminant
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 2
SP - 423
EP - 427
AB - We give an Arakelov theoretic proof of the equality of conductor and discriminant.
LA - eng
KW - Arakelov geometry; conductor and discriminant; arithmetic Noether's formula
UR - http://eudml.org/doc/249267
ER -

References

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  1. S. Bloch, Cycles on arithmetic schemes and Euler characteristics of curves. Proc. of Sympos. Pure Math. 46 (1987) AMS, 421–450. Zbl0654.14004MR927991
  2. T. Chinburg, G. Pappas, M.J. Taylor, ∈ -constants and Arakelov Euler characteristics. Preprint, (1999). Zbl1097.14501
  3. P. Deligne, Le déterminant de la cohomologie. Contemp. Math. 67 (1987), 93–177. Zbl0629.14008MR902592
  4. G. Faltings, Calculus on arithmetic surfaces. Ann. Math. 119 (1984), 387–424. Zbl0559.14005MR740897
  5. W. Fulton, Intersection theory. Springer-Verlag, Berlin, 1984. Zbl0541.14005MR732620
  6. H. Gillet, C. Soulé, An arithmetic Riemann-Roch theorem. Invent. Math. 110 (1992), 473–543. Zbl0777.14008MR1189489
  7. L. Moret-Bailly, La formule de Noether pour les surfaces arithmétiques. Invent. Math. 98 (1989), 499–509. Zbl0727.14014MR1022303
  8. D. Mumford, Stability of projective varieties. Einseign. Math. 23 (1977), 39–100. Zbl0363.14003MR450272
  9. T. Saito, Conductor, discriminant, and the Noether formula of arithmetic surfaces. Duke Math. J. 57 (1988), 151–173. Zbl0657.14017MR952229

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