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arXiv · 1412.7396

A module structure and a vanishing theorem for cycles with modulus

Amalendu Krishna·Jinhyun Park
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Abstract

We show that the higher Chow groups with modulus of Binda-Kerz-Saito for a smooth quasi-projective scheme $X$ is a module over the Chow ring of $X$. From this, we deduce certain pull-backs, the projective bundle formula, and the blow-up formula for higher Chow groups with modulus. We prove vanishing of $0$-cycles of higher Chow groups with modulus on various affine varieties of dimension at least two. This shows in particular that the multivariate analogue of Bloch-Esnault--R\"ulling computations of additive higher Chow groups of 0-cycles vanishes.

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Amalendu Krishna, Jinhyun Park. 2014-12-23. A module structure and a vanishing theorem for cycles with modulus. https://arxiv.org/abs/1412.7396

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