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Rigidity theorem for presheaves with $ \Omega$-transfers


Author: A. Neshitov
Translated by: the author
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 919-932
MSC (2010): Primary 14F43
DOI: https://doi.org/10.1090/spmj/1367
Published electronically: September 21, 2015
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Abstract: In 1983 A. Suslin proved the Quillen-Lichtenbaum conjecture about the algebraic $ K$-theory of algebraically closed fields. The proof was based on a statement called the Suslin rigidity theorem. In the present paper, the rigidity theorem is proved for homotopy invariant presheaves with $ \Omega $-transfers, introduced by I. Panin. This type of presheaves includes the $ K$-functor and algebraic cobordism of M. Levine and F. Morel.


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Additional Information

A. Neshitov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: neshitov@yandex.ru

DOI: https://doi.org/10.1090/spmj/1367
Keywords: Rigidity theorem, presheaves with transfers, cohomology theories
Received by editor(s): January 14, 2014
Published electronically: September 21, 2015
Additional Notes: Supported by RFBR (grant no. 12-01-33057) and by Ontario Trillium Scholarship
Article copyright: © Copyright 2015 American Mathematical Society