On the Profinite Regular Inverse Galois Problem

  • Anna Cadoret

    Université de Bordeaux I, Talence, France


Given a field k, a k-curve X and a k-rational divisor t ⊂ X, we analyze the constraints imposed on X and t by the existence of abelian G-covers f : YX defined over k and unramified outside t. We show that these constraints produce an obstruction to the weak regular inverse Galois problem for a whole class of profinite groups - we call p-obstructed - when k is a finitely generated field of characteristic ≠ p.

Cite this article

Anna Cadoret, On the Profinite Regular Inverse Galois Problem. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1143–1168

DOI 10.2977/PRIMS/1231263782