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Conductors of $ \ell$-adic representations


Author: Douglas Ulmer
Journal: Proc. Amer. Math. Soc. 144 (2016), 2291-2299
MSC (2010): Primary 11F80
DOI: https://doi.org/10.1090/proc/12880
Published electronically: October 5, 2015
MathSciNet review: 3477046
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a new formula for the Artin conductor of an $ \ell $-adic representation of the Weil group of a local field of residue characteristic $ p\neq \ell $.


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  • [Art31] E. Artin, Die gruppentheoretische Struktur der Diskriminanten algebraischer Zahlkörper, J. Reine Angew. Math. 164 (1931), 1–11 (German). MR 1581245, https://doi.org/10.1515/crll.1931.164.1
  • [Cli37] A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math. (2) 38 (1937), no. 3, 533–550. MR 1503352, https://doi.org/10.2307/1968599
  • [DDT97] Henri Darmon, Fred Diamond, and Richard Taylor, Fermat’s last theorem, Current developments in mathematics, 1995 (Cambridge, MA), Int. Press, Cambridge, MA, 1994, pp. 1–154. MR 1474977
    Henri Darmon, Fred Diamond, and Richard Taylor, Fermat’s last theorem, Elliptic curves, modular forms & Fermat’s last theorem (Hong Kong, 1993) Int. Press, Cambridge, MA, 1997, pp. 2–140. MR 1605752
  • [Del73] P. Deligne, Les constantes des équations fonctionnelles des fonctions 𝐿, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 501–597. Lecture Notes in Math., Vol. 349 (French). MR 0349635
  • [DD13] T. Dokchitser and V. Dokchitser, Growth of III in towers for isogenous curves, Compositio Mathematica FirstView (2015), 1-25., https://doi.org/10.1112/S0010437X15007423
  • [Roh94] David E. Rohrlich, Elliptic curves and the Weil-Deligne group, Elliptic curves and related topics, CRM Proc. Lecture Notes, vol. 4, Amer. Math. Soc., Providence, RI, 1994, pp. 125–157. MR 1260960
  • [Ser70] J.-P. Serre,
    Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures),
    Séminaire Delange-Pisot-Poitou: 1969/70, Théorie des Nombres, Fasc. 2, Exp. 19, page 12, Secrétariat mathématique, Paris, 1970.
  • [Ser79] Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237
  • [Ser06] J.-P. Serre.
    Lie algebras and Lie groups, volume 1500 of Lecture Notes in Mathematics.
    Springer-Verlag, Berlin, 2006.
    1964 lectures given at Harvard University, Corrected fifth printing of the second (1992) edition.
  • [ST68] Jean-Pierre Serre and John Tate, Good reduction of abelian varieties, Ann. of Math. (2) 88 (1968), 492–517. MR 0236190, https://doi.org/10.2307/1970722
  • [Tat79] J. Tate, Number theoretic background, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3–26. MR 546607
  • [Wie12] G. Wiese,
    Galois representations,
    Version dated 13 February 2012, downloaded from http://math.uni.lu/˜wiese/notes/GalRep.pdf, 2012.

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Additional Information

Douglas Ulmer
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: ulmer@math.gatech.edu

DOI: https://doi.org/10.1090/proc/12880
Received by editor(s): May 14, 2015
Received by editor(s) in revised form: June 29, 2015
Published electronically: October 5, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society