Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Conductors of $\ell$-adic representations
HTML articles powered by AMS MathViewer

by Douglas Ulmer
Proc. Amer. Math. Soc. 144 (2016), 2291-2299
DOI: https://doi.org/10.1090/proc/12880
Published electronically: October 5, 2015

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 $p\neq \ell$.
References
  • E. Artin, Die gruppentheoretische Struktur der Diskriminanten algebraischer Zahlkörper, J. Reine Angew. Math. 164 (1931), 1–11 (German). MR 1581245, DOI 10.1515/crll.1931.164.1
  • A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math. (2) 38 (1937), no. 3, 533–550. MR 1503352, DOI 10.2307/1968599
  • 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
  • P. Deligne, Les constantes des équations fonctionnelles des fonctions $L$, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 349, Springer, Berlin, 1973, pp. 501–597 (French). MR 0349635
  • T. Dokchitser and V. Dokchitser, Growth of III in towers for isogenous curves, Compositio Mathematica FirstView (2015), 1-25., DOI 10.1112/S0010437X15007423
  • 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, DOI 10.1090/crmp/004/10
  • 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.
  • 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
  • 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.
  • Jean-Pierre Serre and John Tate, Good reduction of abelian varieties, Ann. of Math. (2) 88 (1968), 492–517. MR 236190, DOI 10.2307/1970722
  • 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
  • G. Wiese, Galois representations, Version dated 13 February 2012, downloaded from http://math.uni.lu/˜wiese/notes/GalRep.pdf, 2012.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F80
  • Retrieve articles in all journals with MSC (2010): 11F80
Bibliographic Information
  • Douglas Ulmer
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
  • MR Author ID: 175900
  • ORCID: 0000-0003-1529-4390
  • Email: ulmer@math.gatech.edu
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 2291-2299
  • MSC (2010): Primary 11F80
  • DOI: https://doi.org/10.1090/proc/12880
  • MathSciNet review: 3477046