On an analogue of the fundamental Voevodsky theorem
- Authors: Tyurin D.N.1,2
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Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Leonard Euler International Mathematical Institute at Saint Petersburg (SPB LEIMI), St. Petersburg
- Issue: Vol 89, No 3 (2025)
- Pages: 212-229
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/303963
- DOI: https://doi.org/10.4213/im9659
- ID: 303963
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Abstract
Let $k$ be a field of zero characteristic, $X$ be a $k$-smooth scheme, and $F$be an $\mathbb{A}^1$-invariant quasi-stable presheave with framed transfers.Then the corresponding Gersten complex is exact.
About the authors
Dimitrii Nikolaevich Tyurin
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences; Leonard Euler International Mathematical Institute at Saint Petersburg (SPB LEIMI), St. Petersburg
Author for correspondence.
Email: izv@mi-ras.ru
without scientific degree
References
- V. Voevodsky, “Triangulated categories of motives over a field”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 188–238
- V. Voevodsky, “Cohomological theory of presheaves with transfers”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 87–137
- V. Voevodsky, Notes on framed correspondences, unpublished, 2001, 13 pp.
- G. Garkusha, I. Panin, “Framed motives of algebraic varieties (after V. Voevodsky)”, J. Amer. Math. Soc., 34:1 (2021), 261–313
- G. Garkusha, I. Panin, “Homotopy invariant presheaves with framed transfers”, Camb. J. Math., 8:1 (2020), 1–94
- I. Panin, “Oriented cohomology theories of algebraic varieties. II”, Homology Homotopy Appl., 11:1 (2009), 349–405
- И. А. Панин, “Совершенные тройки и гомотопии отображений мотивных пространств”, Изв. РАН. Сер. матем., 83:4 (2019), 158–193
- F. Morel, V. Voevodsky, “$mathbf A^1$-homotopy theory of schemes”, Inst. Hautes Etudes Sci. Publ. Math., 90 (1999), 45–143
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