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
- PDF | Request permission
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.
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