Alexander Schmidt: Homotopy Invariance of the Tame Homotopy Groups of Regular Schemes

       Author: Alexander Schmidt
       Title: Homotopy Invariance of the Tame Homotopy Groups of Regular Schemes
       in: Preprint (2022)

	Abstract: The étale homotopy groups of schemes as defined by Artin and Mazur have the disadvantage of being homotopy invariant only in characteristic zero. This and other related problems led to the definition of the tame topology which is coarser than the étale topology by disallowing wild ramification along the boundary of compactifications. The objective of this paper is to show that the associated tame homotopy groups are indeed (A1-)homotopy invariant, at least for regular schemes.

Abstract: The étale homotopy groups of schemes as defined by Artin and Mazur have the disadvantage of being homotopy invariant only in characteristic zero. This and other related problems led to the definition of the tame topology which is coarser than the étale topology by disallowing wild ramification along the boundary of compactifications. The objective of this paper is to show that the associated tame homotopy groups are indeed (A1-)homotopy invariant, at least for regular schemes.

pdf-file: homotopy-invariance.ver2
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