Cubic structures and ideal class groups

Pappas, Georgios

doi:10.1016/j.ansens.2005.03.001

Pappas, Georgios

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, pp. 471-503.

EuDML MR Zbl

DOI : 10.1016/j.ansens.2005.03.001

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     author = {Pappas, Georgios},
     title = {Cubic structures and ideal class groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {471--503},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
     number = {3},
     year = {2005},
     doi = {10.1016/j.ansens.2005.03.001},
     mrnumber = {2166342},
     zbl = {1135.11033},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2005.03.001/}
}

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Pappas, Georgios. Cubic structures and ideal class groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, pp. 471-503. doi : 10.1016/j.ansens.2005.03.001. http://www.numdam.org/articles/10.1016/j.ansens.2005.03.001/

Bibliographie
Cité par

[1] Ando M., Hopkins M.J., Strickland N.P., Elliptic spectra, the Witten genus and the theorem of the cube, Invent. Math. 146 (3) (2001) 595-687. | MR | Zbl

[2] Borel A., Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974) 235-272. | Numdam | MR | Zbl

[3] Breen L., Fonctions thêta et théorème du cube, Lecture Notes in Math., vol. 980, Springer, Berlin, 1983. | MR | Zbl

[4] Buhler J., Crandall R., Ernvall R., Metsänkylä T., Irregular primes and cyclotomic invariants to 12 million, J. Symbolic Comput. 31 (1-2) (2001) 89-96. | MR | Zbl

[5] Chinburg T., Pappas G., Taylor M.J., Cubic structures, equivariant Euler characteristics and modular forms, math.NT/0309327.

[6] Demazure M., Gabriel P., Groupes algébriques, Masson et Cie/North-Holland, Paris/Amsterdam, 1970. | MR | Zbl

[7] Deligne P., Le déterminant de la cohomologie, in: Currents Trends in Arithmetical Algebraic Geometry, Contemp. Math., vol. 67, American Mathematical Society, Providence, RI, 1987. | MR | Zbl

[8] Dwyer W., Friedlander E., Algebraic and étale K-theory, Trans. Amer. Math. Soc. 292 (1) (1985) 247-280. | MR | Zbl

[9] Ducrot F., Cube structures and intersection bundles, J. Pure Appl. Algebra 195 (1) (2005) 33-73. | MR | Zbl

[10] Kurihara M., Some remarks on conjectures about cyclotomic fields and K-groups of $Z$ , Compositio Math. 81 (2) (1992) 223-236. | EuDML | Numdam | MR | Zbl

[11] Laumon G., Moret-Bailly L., Champs algébriques, Ergeb. Math. Grenzg. (3), vol. 39, Springer, Berlin, 2000. | MR | Zbl

[12] Lee R., Szczarba R.H., On the torsion in $K_{4} (Z)$ and $K_{5} (Z)$ , Duke Math. J. 45 (1) (1978) 101-129, with an addendum by C. Soulé, 131-132. | MR | Zbl

[13] Mazur B., Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 33-186, (1978). | EuDML | Numdam | MR | Zbl

[14] Mazur B., Wiles A., Class fields of Abelian extensions of $Q$ , Invent. Math. 76 (2) (1984) 179-330. | EuDML | MR | Zbl

[15] Moret-Bailly L., Pinceaux de variétés abéliennes, Astérisque, vol. 129, 1985, 266 pp. | Numdam | MR | Zbl

[16] Pappas G., Galois modules and the theorem of the cube, Invent. Math. 133 (1) (1998) 193-225. | MR | Zbl

[17] Rim D.S., Modules over finite groups, Ann. of Math. 69 (1959) 700-712. | MR | Zbl

[18] Rognes J., $K_{4} (Z)$ is the trivial group, Topology 39 (2) (2000) 267-281. | MR | Zbl

[19] Soulé C., Perfect forms and the Vandiver conjecture, J. reine Angew. Math. 517 (1999) 209-221. | MR | Zbl

[20] , Théorie des topos et cohomologie étale des schémas, Dirigé par Artin M., Grothendieck A., Verdier J.-L. Avec la collaboration de Bourbaki N., Deligne P., Saint-Donat B., Lecture Notes in Math., vols. 269, 270, 305, Springer, Berlin, 1972. | Zbl

[21] , Groupes de monodromie en géométrie algébrique. I, Dirigé par Grothendieck A. Avec la collaboration de Raynaud M., Rim D.S., Lecture Notes in Math., vol. 288, Springer, Berlin, 1972. | MR | Zbl

[22] Washington L., Introduction to Cyclotomic Fields, Graduate Texts in Math., vol. 83, Springer, New York, 1982, xi+389 pp. | MR | Zbl

[23] Waterhouse W., Principal homogeneous spaces and group scheme extensions, Trans. Amer. Math. Soc. 153 (1971) 181-189. | MR | Zbl

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