The homotopy limit problem for Hermitian K-theory, equivariant motivic homotopy theory and motivic Real cobordism |
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| Authors: | P. Hu I. Kriz K. Ormsby |
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| Affiliation: | aWayne State University, Department of Mathematics, 1150 Faculty/Administration Building, 656 W. Kirby, Detroit, MI 48202, United States;bUniversity of Michigan, Department of Mathematics, 2074 East Hall, Ann Arbor, MI, United States;cMassachusetts Institute of Technology, Department of Mathematics, Headquarters Office, Building 2, Room 236, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, United States |
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| Abstract: | The homotopy limit problem for Karoubi?s Hermitian K-theory (Karoubi, 1980) [26] was posed by Thomason (1983) [44]. There is a canonical map from algebraic Hermitian K-theory to the Z/2-homotopy fixed points of algebraic K-theory. The problem asks, roughly, how close this map is to being an isomorphism, specifically after completion at 2. In this paper, we solve this problem completely for fields of characteristic 0 (Theorems 16, 20). We show that the 2-completed map is an isomorphism for fields F of characteristic 0 which satisfy cd2(F[i])<∞, but not in general. |
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| Keywords: | MSC: 14F42 19G38 55P91 |
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