Effective models and extension of torsors over a discrete valuation ring of unequal characteristic

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171706Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p^2-th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y_K\to X_K and let Y be the normalization of X_K in Y. If G=Z/p^n Z, n<3, under some hypothesis on X, we attach some invariants to Y_K \to X_K. If p>2, we determine, through these invariants, when Y\to X has a structure of torsor which extends that of Y_K\to X_K. Moreover we explicitly calculate the effective model (defined by Romagny) of the action of G on Y.40 pages, final version, corrected and improved some statements in the sections 4,5,6 and 7Algebraic GeometryNumber Theory14L15; 14L30; 11G25Effective models and extension of torsors over a discrete valuation ring of unequal characteristictext