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arXiv · 1707.01755

Nice triples and a moving lemma for motivic spaces

Ivan Panin
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Abstract

It is proved that for any cohomology theory A in the sense of [PS] and any essentially k-smooth semi-local X the Cousin complex is exact. As a consequence we prove that for any integer n the Nisnevich sheaf A^n_Nis, associated with the presheaf U |--> A^n(U), is strictly homotopy invariant. Particularly, for any presheaf of S^1-spectra E on the category of k-smooth schemes its Nisnevich sheves of stable A1-homotopy groups are strictly homotopy invariant. The ground field k is arbitrary. We do not use Gabber's presentation lemma. Instead, we use the machinery of nice triples as invented in [PSV] and developed further in [P3]. This recovers a known inaccuracy in Morel's arguments in [M]. The machinery of nice triples is inspired by the Voevodsky machinery of standard triples.

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Ivan Panin. 2017-07-05. Nice triples and a moving lemma for motivic spaces. https://arxiv.org/abs/1707.01755

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