Gras conjecture
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Short description: Result on the p-parts of the Galois eigenspaces of an ideal class group
In algebraic number theory, the Gras conjecture (Gras 1977) relates the p-parts of the Galois eigenspaces of an ideal class group to the group of global units modulo cyclotomic units. It was proved by (Mazur Wiles) as a corollary of their work on the main conjecture of Iwasawa theory. (Kolyvagin 1990) later gave a simpler proof using Euler systems.
References
- Gras, Georges (1977), "Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés", Annales de l'Institut Fourier 27 (1): 1–66, doi:10.5802/aif.641, ISSN 0373-0956, http://aif.cedram.org/item?id=AIF_1977__27_1_1_0
- Kolyvagin, V. A. (1990), "Euler systems", The Grothendieck Festschrift, Vol. II, Progr. Math., 87, Boston, MA: Birkhäuser Boston, pp. 435–483, doi:10.1007/978-0-8176-4575-5_11, ISBN 978-0-8176-3428-5
- Mazur, Barry; Wiles, Andrew (1984), "Class fields of abelian extensions of Q", Inventiones Mathematicae 76 (2): 179–330, doi:10.1007/BF01388599, ISSN 0020-9910
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