2011/09/28 by Alexander Duncan, Zinovy Reichstein, Duncan, Alexander +1 · 4 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1109.6093
We formalize and study several competing notions of versality for an action\nof a linear algebraic group on an algebraic variety X. Our main result is that\nthese notions of versality are equivalent to various statements concerning\nrational points on twisted forms of X (existence of rational points, existence\nof a dense set of rational points, etc.) We give applications of this\nequivalence in both directions, to study versality of group actions and\nrational points on algebraic varieties. We obtain similar results on\np-versality for a prime integer p. An appendix, containing a letter from J.-P.\nSerre, puts the notion of versality in a historical perspective.\n