The conductor of an abelian variety

Armand Brumer; Kenneth Kramer

Compositio Mathematica (1994)

  • Volume: 92, Issue: 2, page 227-248
  • ISSN: 0010-437X

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Brumer, Armand, and Kramer, Kenneth. "The conductor of an abelian variety." Compositio Mathematica 92.2 (1994): 227-248. <http://eudml.org/doc/90305>.

@article{Brumer1994,
author = {Brumer, Armand, Kramer, Kenneth},
journal = {Compositio Mathematica},
keywords = {abelian variety over a -adic field; bounds for the conductor},
language = {eng},
number = {2},
pages = {227-248},
publisher = {Kluwer Academic Publishers},
title = {The conductor of an abelian variety},
url = {http://eudml.org/doc/90305},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Brumer, Armand
AU - Kramer, Kenneth
TI - The conductor of an abelian variety
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 92
IS - 2
SP - 227
EP - 248
LA - eng
KW - abelian variety over a -adic field; bounds for the conductor
UR - http://eudml.org/doc/90305
ER -

References

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  1. 1 A. Brumer: The rank of J0(N). Submitted to Astérisque. Zbl0851.11035MR1330927
  2. 2 C.W. Curtis and I. Reiner: Methods of Representation Theory. 2 vols. John Wiley, New York, 1987. Zbl0616.20001MR892316
  3. 3 J.-M. Fontaine: Groupes de ramification et représentation d'Artin. Ann. Sci. E.N.S. (4) 4 (1971) 337-392. Zbl0232.12006MR289458
  4. 4 A. Grothendieck: Modèles de Néron et monodromie. SGA 7, Exposé IX, Lecture Notes in Math. 288, 313-523, Springer-Verlag: Berlin, New York, 1970. Zbl0248.14006MR354656
  5. 5 B. Huppert: Endliche Gruppen I. Springer-Verlag: Berlin, New York, 1967. Zbl0217.07201MR224703
  6. 6 H W. Lenstra, F.Oort: Abelian varieties having purely additive reduction. J. Pure and Applied Algebra36 (1985) 281-298. Zbl0557.14022MR790619
  7. 7 P. Lockhart, M.I. Rosen, J. Silverman: An upper bound for the conductor of an abelian variety. Journal of Algebraic Geometry2 (1993) 569-601. Zbl0816.14021MR1227469
  8. 8 D. Lorenzini: Groups of components of Néron models of Jacobians. Compositio Math.73 (1990) 145-160. Zbl0737.14008MR1046735
  9. 9 J. Milne: The arithmetic of abelian varieties. Inv. Math.17 (1972) 177-190. Zbl0249.14012MR330174
  10. 10 F. Oort: Good and stable reduction of abelian varieties. Manuscripta Math.11 (1974) 171-197. Zbl0266.14016MR347834
  11. 11 O. Ore: Abriss einer arithmetischen theorie der Galoischen Körper. Math. Ann.100 (1928) 650-673. Zbl54.0154.01MR1512509JFM55.0697.16
  12. 12 S. Sen: Ramification in p-adic Lie extensions. Inv. Math.17 (1972) 44-50. Zbl0242.12012MR319949
  13. 13 J.-P. Serre: Corps locaux. Hermann, Paris, 1962, or Grad. Texts in Math. 67, Springer-Verlag: Berlin, New York, 1979. Zbl0423.12016MR150130
  14. 14 J.-P. Serre: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Inv. Math.15 (1972) 259-331. Zbl0235.14012MR387283
  15. 15 J.-P. Serre: Sur les représentations modulaires de degré 2 de Gal(Q/Q). Duke Math. J.54 (1987) 179-230. Zbl0641.10026MR885783
  16. 16 J.-P. Serre, J. Tate: Good reduction of abelian varieties. Annals of Mathematics88 (1968) 492-517. Zbl0172.46101MR236190
  17. 17 T. Saito*: Conductor, discriminant and the Noether formula for arithmetic surfaces. Duke Math. J.57 (1988) 151-173. Zbl0657.14017MR952229

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