Journal
JOURNAL OF ALGEBRAIC GEOMETRY
Volume 24, Issue 3, Pages 499-530Publisher
UNIV PRESS INC
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Funding
- National Science Foundation RTG [DMS 0838697, DMS 0943832]
- National Sciences and Engineering Research Council of Canada Discovery grant [250217-2012]
- [CTKPR11]
- Direct For Mathematical & Physical Scien [943832] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [943832] Funding Source: National Science Foundation
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We formalize and study several competing notions of versality for an action of a linear algebraic group on an algebraic variety X. Our main result is that these notions of versality are equivalent to various statements concerning rational points on twisted forms of X (existence of rational points, existence of a dense set of rational points, etc.). We give applications of this equivalence in both directions to study versality of group actions and rational points on algebraic varieties. We obtain similar results on p-versality for a prime integer p. An appendix, containing a letter from J.-P. Serre, puts the notion of versality in a historical perspective.
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