Elliptic curves and local ϵ -factors

K. Kramer; J. Tunnell

Compositio Mathematica (1982)

  • Volume: 46, Issue: 3, page 307-352
  • ISSN: 0010-437X

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Kramer, K., and Tunnell, J.. "Elliptic curves and local $\epsilon $-factors." Compositio Mathematica 46.3 (1982): 307-352. <http://eudml.org/doc/89555>.

@article{Kramer1982,
author = {Kramer, K., Tunnell, J.},
journal = {Compositio Mathematica},
keywords = {norm index; elliptic curve; local field; Weil-Deligne group; epsilon factors; global field; Tate-Shafarevich group},
language = {eng},
number = {3},
pages = {307-352},
publisher = {Martinus Nijhoff Publishers},
title = {Elliptic curves and local $\epsilon $-factors},
url = {http://eudml.org/doc/89555},
volume = {46},
year = {1982},
}

TY - JOUR
AU - Kramer, K.
AU - Tunnell, J.
TI - Elliptic curves and local $\epsilon $-factors
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 46
IS - 3
SP - 307
EP - 352
LA - eng
KW - norm index; elliptic curve; local field; Weil-Deligne group; epsilon factors; global field; Tate-Shafarevich group
UR - http://eudml.org/doc/89555
ER -

References

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  2. [2] B. BIRCH and W. KUYK Editors: Modular functions of one variable IV. Lecture Notes in Math.475, Springer-Verlag1975. Zbl0315.14014MR376533
  3. [3] P. Deligne: Formes modulaires et representations de GL(2), in Modular functions of one variable II. Lecture Notes in Math. 349, Springer-Verlag1973, 55-106. Zbl0271.10032MR347738
  4. [4] P. Deligne: Les constantes des equations fonctionelles des fonctions L, in Modular functions of one variable II. Lecture Notes in Math. 349, Springer-Verlag1973, 501-579. Zbl0271.14011MR349635
  5. [5] P. Deligne: Les constantes locales de l'equation fonctionelle de la fonction L d'Artin d'une representation orthogonale. Inv. Math.35 (1976) 299-316. Zbl0337.12012MR506172
  6. [6] A. Frohlich and J. Queyrut: On the functional equation of the Artin L-function for characters of real representations. Inv. Math.20 (1973) 125-138. Zbl0256.12010MR321888
  7. [7] K. Kramer: Two descent for elliptic curves in characteristic two. Trans. AMS232 (1977) 279-295. Zbl0327.14007MR441977
  8. [8] K. Kramer: Arithmetic of elliptic curves upon quadratic extension. Trans. AMS.264 (1981) 121-135. Zbl0471.14020MR597871
  9. [9] S. Lang: Algebraic groups over finite fields. Amer. J. Math.78, no. 3 (1956) 555-563. Zbl0073.37901MR86367
  10. [10] R. Langlands: Modular forms and l-adic representations, in Modular functions of one variable II. Lecture Notes in Math. 349, Springer-Verlag1973, 361-500. Zbl0279.14007MR354617
  11. [11] B. Mazur: Rational points of Abelian varieties with values in towers of number fields. Inv. Math.18 (1972) 183-266. Zbl0245.14015MR444670
  12. [12] J. Milne: Weil-Châtelet groups over local fields. Ann. Sci. Ecole Norm. Sup.4 (1970) 273-284. Zbl0212.53201MR276249
  13. [13] A. Ogg: Elliptic curves and wild ramification. Amer. J. Math. (1967) 1-21. Zbl0147.39803MR207694
  14. (14) J-P. Serre ! Corps Locaux, 2nd Edition, Hermann, Paris1968. MR354618
  15. [15] J-P. Serre and J. Tate: Good reduction of abelian varieties. Annals of Math.88 (1968) 492-517. Zbl0172.46101MR236190
  16. [16] J. Tate: The arithmetic of elliptic curves. Inv. Math.23 (1974) 179-206. Zbl0296.14018MR419359
  17. [17] J. Tate: Algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular functions of one variable IV. Lecture Notes in Math. 476, Springer-Verlag1975. Zbl1214.14020MR393039
  18. [18] J. Tate: Number theoretic background, in Automorphic Forms, Representations and L-functions, Proc. Symp. in Pure Math. XXXIII Part2 (1979) 3-26. Zbl0422.12007MR546607

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