DOI

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.

Язык оригиналаанглийский
Страницы (с-по)3195-3218
Число страниц24
ЖурналJournal of Pure and Applied Algebra
Том222
Номер выпуска10
DOI
СостояниеОпубликовано - окт 2018

    Предметные области Scopus

  • Алгебра и теория чисел

ID: 36094678