Gras conjecture
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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 (1984) as a corollary of their work on the main conjecture of Iwasawa theory. Kolyvagin (1990) later gave a simpler proof using Euler systems. A version of the Gras conjecture applying to ray class groups was later proven by Timothy All.
- Gras, Georges (1977), , Annales de l'Institut Fourier, 27 (1): 1–66, doi:, ISSN , MR
- Kolyvagin, V. A. (1990), "Euler systems", The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Boston, MA: Birkhäuser Boston, pp. 435–483, doi:, ISBN 978-0-8176-3428-5, MR
- Mazur, Barry; Wiles, Andrew (1984), "Class fields of abelian extensions of Q", Inventiones Mathematicae, 76 (2): 179–330, Bibcode:, doi:, ISSN , MR , S2CID