Weil restriction, normal bundles and motivic Thom spaces

Fuente: arXiv
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Autore principale: Zhu, Guangzhao
Natura: Preprint
Pubblicazione: 2026
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author Zhu, Guangzhao
author_facet Zhu, Guangzhao
contents Recent developments in motivic homotopy theory, particularly the construction of norm functors by Bachmann and Hoyois, have revealed deep connections between algebraic geometry and homotopy-theoretic structures. In this paper, we investigate certain geometric aspects of norm functors through the Weil restriction of schemes, which underlies these constructions. We show that Weil restriction preserves vector bundles and extend existing results concerning normal bundles. We then relate the Weil restriction to norm functors and, using a result of Bachmann and Hoyois, establish its compatibility with motivic Thom spaces. Finally, in the setting of motivic cohomology with rational coefficients, we prove that the Weil restriction map agrees with the norm map induced by a norm functor and that it preserves Thom classes.
format Preprint
id arxiv_https___arxiv_org_abs_2603_22199
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Weil restriction, normal bundles and motivic Thom spaces
Zhu, Guangzhao
Algebraic Geometry
Algebraic Topology
14F42
Recent developments in motivic homotopy theory, particularly the construction of norm functors by Bachmann and Hoyois, have revealed deep connections between algebraic geometry and homotopy-theoretic structures. In this paper, we investigate certain geometric aspects of norm functors through the Weil restriction of schemes, which underlies these constructions. We show that Weil restriction preserves vector bundles and extend existing results concerning normal bundles. We then relate the Weil restriction to norm functors and, using a result of Bachmann and Hoyois, establish its compatibility with motivic Thom spaces. Finally, in the setting of motivic cohomology with rational coefficients, we prove that the Weil restriction map agrees with the norm map induced by a norm functor and that it preserves Thom classes.
title Weil restriction, normal bundles and motivic Thom spaces
topic Algebraic Geometry
Algebraic Topology
14F42
url https://arxiv.org/abs/2603.22199