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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 443, Pages 5–8 (Mi znsl6252)  
On the zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety

A. S. Ananyevskiy

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
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Abstract: The zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety is computed. This group is identified with the group of oriented zero-cycles on the variety. The proof heavily exploits properties of strictly homotopy invariant sheaves.
Key words and phrases: $\mathbb A^1$-homotopy, oriented cycles, motives.
Funding agency Grant number
Russian Science Foundation 14-11-00456
Received: 02.12.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 222, Issue 4, Pages 367–369
DOI: https://doi.org/10.1007/s10958-017-3306-7
Bibliographic databases:
Document Type: Article
UDC: 512.73
Language: Russian
Citation: A. S. Ananyevskiy, “On the zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety”, Problems in the theory of representations of algebras and groups. Part 29, Zap. Nauchn. Sem. POMI, 443, POMI, St. Petersburg, 2016, 5–8; J. Math. Sci. (N. Y.), 222:4 (2017), 367–369
Citation in format AMSBIB
\Bibitem{Ana16}
\by A.~S.~Ananyevskiy
\paper On the zeroth stable $\mathbb A^1$-homotopy group of a~smooth projective variety
\inbook Problems in the theory of representations of algebras and groups. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 443
\pages 5--8
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6252}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3507760}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 222
\issue 4
\pages 367--369
\crossref{https://doi.org/10.1007/s10958-017-3306-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014750444}
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