Abhyankar's conjecture

Not to be confused with Abhyankar's lemma.

In abstract algebra, Abhyankar's conjecture is a conjecture of Shreeram Abhyankar posed in 1957, on the Galois groups of algebraic function fields of characteristic p.[1] The soluble case was solved by Serre in 1990[2] and the full conjecture was proved in 1994 by work of Michel Raynaud and David Harbater.[3][4][5]

  1. ^ Abhyankar, Shreeram (1957), "Coverings of Algebraic Curves", American Journal of Mathematics, 79 (4): 825–856, doi:10.2307/2372438.
  2. ^ Serre, Jean-Pierre (1990), "Construction de revêtements étales de la droite affine en caractéristique p", Comptes Rendus de l'Académie des Sciences, Série I (in French), 311 (6): 341–346, Zbl 0726.14021
  3. ^ Raynaud, Michel (1994), "Revêtements de la droite affine en caractéristique p > 0", Inventiones Mathematicae, 116 (1): 425–462, Bibcode:1994InMat.116..425R, doi:10.1007/BF01231568, Zbl 0798.14013.
  4. ^ Harbater, David (1994), "Abhyankar's conjecture on Galois groups over curves", Inventiones Mathematicae, 117 (1): 1–25, Bibcode:1994InMat.117....1H, doi:10.1007/BF01232232, Zbl 0805.14014.
  5. ^ Fried, Michael D.; Jarden, Moshe (2008), Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 11 (3rd ed.), Springer-Verlag, p. 70, ISBN 978-3-540-77269-9, Zbl 1145.12001