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 : Y → X 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. 1143–1168DOI 10.2977/PRIMS/1231263782