Haine, Peter J. and Holzschuh, Tim and Wolf, Sebastian (2024) Nonabelian basechange theorems and étale homotopy theory. JOURNAL OF TOPOLOGY, 17 (4): e70009. ISSN 1753-8416, 1753-8424
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This paper has two main goals. First, we prove nonabelian refinements of basechange theorems in & eacute;tale cohomology (i.e., prove analogues of the classical statements for sheaves of spaces). Second, we apply these theorems to prove a number of results about the & eacute;tale homotopy type. Specifically, we prove nonabelian refinements of the smooth basechange theorem, Huber-Gabber affine analogue of the proper basechange theorem, and Fujiwara-Gabber rigidity theorem. Our methods also recover Chough's nonabelian refinement of the proper basechange theorem. Transporting an argument of Bhatt-Mathew to the nonabelian setting, we apply nonabelian proper basechange to show that the profinite & eacute;tale homotopy type satisfies arc-descent. Using nonabelian smooth and proper basechange and descent, we give rather soft proofs of a number of K & uuml;nneth formulas for the & eacute;tale homotopy type.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DESCENT; RAMIFICATION; GEOMETRY |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Dec 2025 07:04 |
| Last Modified: | 09 Dec 2025 07:04 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64584 |
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