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On the zeroth stable A1-homotopy group of a smooth curve. / Ананьевский, Алексей Сергеевич.
в: Journal of Pure and Applied Algebra, Том 222, № 10, 10.2018, стр. 3195-3218.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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