Torsion orders of complete intersections
Abstract
By a classical result of Roitman, a complete intersection of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer , when viewed as a cycle in the Chow group, has support in , for some divisor and a finite set of closed points . The minimal such is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Th\'el\`ene and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Koll\'ar and Totaro to show lower bounds for the very general complete intersection.
Cite
@article{arxiv.1605.01913,
title = {Torsion orders of complete intersections},
author = {Andre Chatzistamatiou and Marc Levine},
journal= {arXiv preprint arXiv:1605.01913},
year = {2018}
}
Comments
50 pages. A reference to the paper by Bruno Kahn, "Torsion order of smooth projective surfaces, with an appendix by J.L. Colliot-Th\'el\`ene" arXiv:1605.01762 [math.AG], was added and some typos corrected. Fixed a gap in the proof of the second main theorem. The statement of the second main theorem was modified in order to exclude the odd dimensional case when the prime 2 is considered