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arXiv · 2108.13594

On extension of the motivic cohomology beyond smooth schemes

Jinhyun Park
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Abstract

We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on the category, that it detects nilpotence, and that its restriction to the subcategory of smooth schemes agrees with the pre-existing motivic cohomology theory, which is the higher Chow theory of S. Bloch (Adv. Math., 1986). A few structures and applications are discussed.

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Jinhyun Park. 2021-08-31. On extension of the motivic cohomology beyond smooth schemes. https://arxiv.org/abs/2108.13594

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