Cousin complex on the complement to the strict normal-crossing divisor in a local essentially smooth scheme over a field

Author:

Druzhinin Andrei Eduardovich1

Affiliation:

1. St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract

For any $\mathbb{A}^1$-invariant cohomology theory that satisfies Nisnevich excision on the category of smooth schemes over a field $k$ it is proved that the Cousin complex on the complement $U-D$ to the strict normal-crossing divisor $D$ in a local essentially smooth scheme $U$ is acyclic. This claim is also proved for the schemes $(X-D)\times(\mathbb{A}^1_k-Z_0)\times…\times(\mathbb{A}^1_k-Z_l)$, where $Z_0,…,Z_l$ is a finite family of closed subschemes in the affine line over $k$. Bibliography: 32 titles.

Funder

Russian Science Foundation

Contest «Young Russian Mathematics»

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

Reference39 articles.

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2. Higher algebraic K-theory: I

3. Adv. Lect. Math. (ALM);D. Quillen,2010

4. The equicharacteristic case of the Gersten conjecture;I. A. Panin,2003

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