Varieties and pure symbols

Alexander Vishik

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arXiv · 2509.00592

Varieties and pure symbols

Alexander Vishik

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Abstract

In this article, we prove that the 2-isotropy of any projective variety is controlled by a pure symbol in the Milnor's K-theory (mod 2) of the flexible closure of the base field. We also show that such pure symbols control the 2-equivalence of field extensions as well as the numerical equivalence of algebraic cycles (with mod 2 coefficients).

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Alexander Vishik. 2025-08-30. Varieties and pure symbols. https://arxiv.org/abs/2509.00592

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