Geodesic
Thaine's Method for Circular Units and a Conjecture of Gross
Canadian journal of mathematics, Tome 47 (1995) no. 2, pp. 302-317

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1995-016-6
Mots-clés : 11R11, 11R04, 11R18, 11R27, 11R29 
Darmon, Henri. Thaine's Method for Circular Units and a Conjecture of Gross. Canadian journal of mathematics, Tome 47 (1995) no. 2, pp. 302-317. doi: 10.4153/CJM-1995-016-6
@article{10_4153_CJM_1995_016_6,
     author = {Darmon, Henri},
     title = {Thaine's {Method} for {Circular} {Units} and a {Conjecture} of {Gross}},
     journal = {Canadian journal of mathematics},
     pages = {302--317},
     year = {1995},
     volume = {47},
     number = {2},
     doi = {10.4153/CJM-1995-016-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-016-6/}
}
TY  - JOUR
AU  - Darmon, Henri
TI  - Thaine's Method for Circular Units and a Conjecture of Gross
JO  - Canadian journal of mathematics
PY  - 1995
SP  - 302
EP  - 317
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-016-6/
DO  - 10.4153/CJM-1995-016-6
ID  - 10_4153_CJM_1995_016_6
ER  - 
%0 Journal Article
%A Darmon, Henri
%T Thaine's Method for Circular Units and a Conjecture of Gross
%J Canadian journal of mathematics
%D 1995
%P 302-317
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-016-6/
%R 10.4153/CJM-1995-016-6
%F 10_4153_CJM_1995_016_6

[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

Cité par Sources :