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Injectivity theorem for homotopy invariant presheafs with Witt-transfers


Author: K. Chepurkin
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 28 (2016), nomer 2.
Journal: St. Petersburg Math. J. 28 (2017), 291-297
MSC (2010): Primary 19G12; Secondary 11E81
DOI: https://doi.org/10.1090/spmj/1451
Published electronically: February 15, 2017
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Abstract: A definition of the category of Witt-correspondences over a field of characteristic different from 2 is given, the presheafs with Witt-transfers are introduced, and a series of general properties of these objects are established. In Theorem 1, the injectivity theorem is shown to be true for a homotopy invariant presheaf with Witt-transfers and for the local ring of a smooth variety. As a consequence, the injectivity theorem is proved for the Witt functor.


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Additional Information

K. Chepurkin
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
Email: chekanumn@mail.ru

DOI: https://doi.org/10.1090/spmj/1451
Keywords: Quadratic form, Witt functor, Witt-correspondence, homotopy, presheaf
Received by editor(s): May 23, 2014
Published electronically: February 15, 2017
Additional Notes: Supported by RFBR (grant no. 14-01-31095)
Article copyright: © Copyright 2017 American Mathematical Society