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

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

2008-03-26

arxiv.org/abs/0803.3730v2

Internat. Math. Res. Not. (2008); Vol. 2008, article ID:rnn111, 68 pages

Mathematics

Algebraic Geometry

40 pages, final version, corrected and improved some statements in the sections 4,5,6 and 7

Scientific paper

Let 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.

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