Injectivity theorem for homotopy invariant presheafs with Witt-transfers
HTML articles powered by AMS MathViewer
- by
K. Chepurkin
Translated by: A. Plotkin - St. Petersburg Math. J. 28 (2017), 291-297
- DOI: https://doi.org/10.1090/spmj/1451
- Published electronically: February 15, 2017
- PDF | Request permission
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.References
- Ernst Witt, Theorie der quadratischen Formen in beliebigen Körpern, J. Reine Angew. Math. 176 (1937), 31–44 (German). MR 1581519, DOI 10.1515/crll.1937.176.31
- Manfred Knebusch, Symmetric bilinear forms over algebraic varieties, Conference on Quadratic Forms—1976 (Proc. Conf., Queen’s Univ., Kingston, Ont., 1976) Queen’s Papers in Pure and Appl. Math., No. 46, Queen’s Univ., Kingston, Ont., 1977, pp. 103–283. MR 0498378
- Paul Balmer, Triangular Witt groups. I. The 12-term localization exact sequence, $K$-Theory 19 (2000), no. 4, 311–363. MR 1763933, DOI 10.1023/A:1007844609552
- —, Triangular Witt groups. Pt. II. From usual to derived, Math. Z. 236 (2001), no. 2, 351–382. MR 18115833 (2002h:19003)
- Stefan Gille and Alexander Nenashev, Pairings in triangular Witt theory, J. Algebra 261 (2003), no. 2, 292–309. MR 1966631, DOI 10.1016/S0021-8693(02)00669-5
- Alexander Nenashev, Projective push-forwards in the Witt theory of algebraic varieties, Adv. Math. 220 (2009), no. 6, 1923–1944. MR 2493184, DOI 10.1016/j.aim.2008.11.013
- Manuel Ojanguren, Quadratic forms over regular rings, J. Indian Math. Soc. (N.S.) 44 (1980), no. 1-4, 109–116 (1982). MR 752647
- Allen Altman and Steven Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Mathematics, Vol. 146, Springer-Verlag, Berlin-New York, 1970. MR 0274461
- Manuel Ojanguren and Ivan Panin, A purity theorem for the Witt group, Ann. Sci. École Norm. Sup. (4) 32 (1999), no. 1, 71–86 (English, with English and French summaries). MR 1670591, DOI 10.1016/S0012-9593(99)80009-3
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
Bibliographic Information
- K. Chepurkin
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
- Email: chekanumn@mail.ru
- Received by editor(s): May 23, 2014
- Published electronically: February 15, 2017
- Additional Notes: Supported by RFBR (grant no. 14-01-31095)
- © Copyright 2017 American Mathematical Society
- Journal: St. Petersburg Math. J. 28 (2017), 291-297
- MSC (2010): Primary 19G12; Secondary 11E81
- DOI: https://doi.org/10.1090/spmj/1451
- MathSciNet review: 3593010