Homotopy Invariance of the Sheaf W Nis and of Its Cohomology | Zendy

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Homotopy Invariance of the Sheaf W Nis and of Its Cohomology

Author(s) -

Ivan Panin

Publication year - 2010

Publication title -

developments in mathematics

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.442

H-Index - 17

eISSN - 2197-795X

pISSN - 1389-2177

DOI - 10.1007/978-1-4419-6211-9_21

Subject(s) - mathematics , sheaf , cohomology , homotopy group , homotopy , pure mathematics , invariant (physics) , sheaf cohomology , homotopy category , eilenberg–maclane space , conjecture , homotopy sphere , whitehead theorem , group cohomology , mathematical physics

A conjecture of F. Morel states that the motivic group π0, 0(k) of a field k coincides with the Grothendieck-Witt group GW(k) of quadratic forms over k provided that char(k)≠2. Morel’s proof of the conjecture is based among others on the the following result: the Nisnevich sheaf W Nis associated with the presheaf X↦W(X) is homotopy invariant and all its Nisnevich cohomology are homotopy invariant too. A rather short and self-contained proof of the result is given here.

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