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arXiv · 1605.01913

Torsion orders of complete intersections

Andre Chatzistamatiou·Marc Levine
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Abstract

By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X\times D\cup F\times X$, for some divisor $D$ and a finite set of closed points $F$. The minimal such $N$ 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.

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BibTeXRIS

Andre Chatzistamatiou, Marc Levine. 2016-05-06. Torsion orders of complete intersections. https://doi.org/10.2140/ant.2017.11.1779

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