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Thaine's Method for Circular Units and a Conjecture of Gross

Published online by Cambridge University Press:  20 November 2018

Henri Darmon
Henri Darmon*
Affiliation:
Department of Mathematics Princeton University Princeton, New Jersey 08540 U.S.A
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Abstract

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We formulate a conjecture analogous to Gross' refinement of the Stark conjectures on special values of abelian L-series at s = 0. Some evidence for the conjecture can be obtained, thanks to the fundamental ideas of F. Thaine.

Keywords

11R1111R0411R1811R2711R29
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 302 - 317
Copyright
Copyright © Canadian Mathematical Society 1995

References

[DR] Deligne, P. and Ribet, K., Values ofabelian L-functions at negative integers over totally real fields, Invent. Math. 59(1980), 227–286.Google Scholar
[Gr] Gross, B.H., On the values ofabelian L-functions at s = 0, J. Fac. Sci. Univ. Tokyo Sect. IA Math. (1) 35(1988), 177–197.Google Scholar
[HI] Hales, Alfred W., Augmentation terminals of finite abelian groups. In: SLN 1006, 1983. 720–733.Google Scholar
[H2] Hales, Alfred W., Stable augmentation quotients ofabelian groups, Pacific J. Math. (2) 118(1985), 401–410.Google Scholar
[Iw] Iwasawa, K., On Zrextensions of algebraic number fields, Ann. of Math. (2) 98(1973).Google Scholar
[Ko] Kolyvagin, V.A., Euler Systems, Birkhâuser volume in honor of Grothendieck, to appear.Google Scholar
[La] Lang, S., Cyclotomic fields I and II, combined second edition, Graduate Texts in Math. 121, Springer-Verlag, 1990.Google Scholar
[MT] Mazur, B. and Tate, J., Refined conjectures of the “Birch and Swinnerton-Dyer type”, Duke Math. J. (2) 54(1987), p. 711.Google Scholar
[Pa] Passi, I.B.S, Group rings and their augmentation ideals, SLN 715, Berlin, New York, 1979.Google Scholar
[Ru] Rubin, K.C., Global units and ideal class groups, Invent. Math. 89( 1987), 511–526.Google Scholar
[Sch] Schoof, R., preprint.Google Scholar
[Th] Thaine, F., On the ideal class groups of real abelian number fields, Ann. of Math. 128(1988), 1–18.Google Scholar
[Wa] Washington, L., Introduction to cyclotomic fie Ids, Graduate Texts in Math. 83, Springer-Verlag, New York, 1982.Google Scholar