کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897394 | 1630739 | 2018 | 24 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the zeroth stable A1-homotopy group of a smooth curve
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We provide a cohomological interpretation of the zeroth stable A1-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 A1-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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3195-3218
Journal: Journal of Pure and Applied Algebra - Volume 222, Issue 10, October 2018, Pages 3195-3218
نویسندگان
Alexey Ananyevskiy,