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On the zeroth stable A1-homotopy group of a smooth curve. / Ананьевский, Алексей Сергеевич.

In: Journal of Pure and Applied Algebra, Vol. 222, No. 10, 10.2018, p. 3195-3218.

Research output: Contribution to journal › Article › peer-review

Harvard

Ананьевский, АС 2018, 'On the zeroth stable A1-homotopy group of a smooth curve', Journal of Pure and Applied Algebra, vol. 222, no. 10, pp. 3195-3218. https://doi.org/10.1016/j.jpaa.2017.12.001

APA

Ананьевский, А. С. (2018). On the zeroth stable A1-homotopy group of a smooth curve. Journal of Pure and Applied Algebra, 222(10), 3195-3218. https://doi.org/10.1016/j.jpaa.2017.12.001

Vancouver

Ананьевский АС. On the zeroth stable A1-homotopy group of a smooth curve. Journal of Pure and Applied Algebra. 2018 Oct;222(10):3195-3218. https://doi.org/10.1016/j.jpaa.2017.12.001

Author

Ананьевский, Алексей Сергеевич. / On the zeroth stable A1-homotopy group of a smooth curve. In: Journal of Pure and Applied Algebra. 2018 ; Vol. 222, No. 10. pp. 3195-3218.

BibTeX

@article{8a62e9f08b264678a09c459b9b00c950,
title = "On the zeroth stable A1-homotopy group of a smooth curve",
abstract = "We provide a cohomological interpretation of the zeroth stable A 1-homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic to the first Nisnevich (or Zariski) cohomology group of a certain sheaf closely related to the first Milnor–Witt K-theory sheaf. This cohomology group can be computed using an explicit Gersten-type complex. We show that if the base field is algebraically closed then the zeroth stable A 1-homotopy group of a smooth curve coincides with the zeroth Suslin homology group that was identified by Suslin and Voevodsky with a relative Picard group. As a consequence we reobtain a version of Suslin's rigidity theorem. ",
author = "Ананьевский, {Алексей Сергеевич}",
note = "Funding Information: I would like to thank the participants of the A 1 -homotopy theory seminar in Chebyshev Laboratory and especially Mikhail Bondarko, Ivan Panin and Vladimir Sosnilo for valuable comments and suggestions. The research is supported by the Russian Science Foundation grant No. 14-21-00035 . Appendix A",
year = "2018",
month = oct,
doi = "10.1016/j.jpaa.2017.12.001",
language = "English",
volume = "222",
pages = "3195--3218",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "10",

}

RIS

TY - JOUR

T1 - On the zeroth stable A1-homotopy group of a smooth curve

AU - Ананьевский, Алексей Сергеевич

N1 - Funding Information: I would like to thank the participants of the A 1 -homotopy theory seminar in Chebyshev Laboratory and especially Mikhail Bondarko, Ivan Panin and Vladimir Sosnilo for valuable comments and suggestions. The research is supported by the Russian Science Foundation grant No. 14-21-00035 . Appendix A

PY - 2018/10

Y1 - 2018/10

N2 - We provide a cohomological interpretation of the zeroth stable A 1-homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic to the first Nisnevich (or Zariski) cohomology group of a certain sheaf closely related to the first Milnor–Witt K-theory sheaf. This cohomology group can be computed using an explicit Gersten-type complex. We show that if the base field is algebraically closed then the zeroth stable A 1-homotopy group of a smooth curve coincides with the zeroth Suslin homology group that was identified by Suslin and Voevodsky with a relative Picard group. As a consequence we reobtain a version of Suslin's rigidity theorem.

AB - We provide a cohomological interpretation of the zeroth stable A 1-homotopy group of a smooth curve over an infinite perfect field. We show that this group is isomorphic to the first Nisnevich (or Zariski) cohomology group of a certain sheaf closely related to the first Milnor–Witt K-theory sheaf. This cohomology group can be computed using an explicit Gersten-type complex. We show that if the base field is algebraically closed then the zeroth stable A 1-homotopy group of a smooth curve coincides with the zeroth Suslin homology group that was identified by Suslin and Voevodsky with a relative Picard group. As a consequence we reobtain a version of Suslin's rigidity theorem.

UR - http://www.scopus.com/inward/record.url?scp=85039150230&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2017.12.001

DO - 10.1016/j.jpaa.2017.12.001

M3 - Article

VL - 222

SP - 3195

EP - 3218

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 10

ER -

ID: 36094678