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The projective bundle theorem for Ij -cohomology

Published online by Cambridge University Press:  04 April 2013

Jean Fasel
Jean Fasel*
Affiliation:
Mathematisches Institut der Universität München, Theresienstrasse 39, D-80333 Münchenjean.fasel@gmail.comhttp://www.mathematik.uni-muenchen.de/~fasel/
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Abstract

We compute the total Ij -cohomology of a projective bundle over a smooth scheme.

Keywords

Projective bundlesIj -cohomologyquadratic formsGersten complexPrimary: 14C2514F4319G38

Information

Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 2 , April 2013 , pp. 413 - 464
Copyright
Copyright © ISOPP 2013 

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References

1.Balmer, Paul. Witt cohomology, Mayer-Vietoris, homotopy invariance and the Gersten conjecture. K-Theory 23 (1) (2001), 15–30.Google Scholar
2.Balmer, Paul. Products of degenerate quadratic forms. Compos. Math. 141 (6) (2005), 1374–1404.Google Scholar
3.Balmer, Paul. Witt groups. In Handbook of K-theory 1, 2, pages 539–576. Springer, Berlin, 2005.Google Scholar
4.Balmer, Paul and Calmès, Baptiste. Geometric description of the connecting homomorphism for Witt groups. Doc. Math. 14 (2009), 525–550.Google Scholar
5.Balmer, Paul and Gille, Stefan. Koszul complexes and symmetric forms over the punctured affine space. Proc. London Math. Soc. (3) 91 (2) (2005), 273–299.Google Scholar
6.Balmer, Paul and Walter, Charles. A Gersten-Witt spectrals equence for regular schemes. Ann. Sci. École Norm. Sup. (4) 35 (1) (2002), 127–152.Google Scholar
7.Brosnan, Patrick. Steenrod operations in Chow theory. Trans. Amer. Math. Soc. 355 (5) (2003), 1869–1903 (electronic).Google Scholar
8.Fasel, Jean. The Chow-Witt ring. Doc. Math. 12 (2007), 275–312 (electronic).Google Scholar
9.Fasel, Jean. Groupes de Chow-Witt. Mém. Soc. Math. Fr. (N.S.) 113 (2008), viii+197.Google Scholar
10.Fasel, Jean. The excess intersection formula for Grothendieck-Witt groups. Manuscripta Math. 130 (4) (2009), 411–423.Google Scholar
11.Fulton, William. Intersection theory, volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin, second edition, 1998.Google Scholar
12.Gille, Stefan. A graded Gersten-Witt complex for s chemes with a dualizing complex and the Chow group. J. Pure Appl. Algebra 208 (2) (2007), 391–419.Google Scholar
13.Gille, Stefan and Hornbostel, Jens. A zero theorem for the transfer of coherent Witt groups. Math. Nachr. 278 (7-8) (2005), 815–823.Google Scholar
14.Grothendieck, Alexandre. Éléments de géométrie algèbrique: II. Étude globale élémentaire de quelques classes de morphismes. Publ. M ath. Inst. Hautes Études Sci. 8 (1961), 5–222.Google Scholar
15.Hartshorne, Robin. Algebraic geometry. Springer-Verlag, New York, 1977. Graduate Texts in Mathematics 52.Google Scholar
16.Kato, Kazuya. Milnor K-theory and the Chow group of zero cycles. In Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math. 55, pages 241–253. Amer. Math. Soc., Providence, RI, 1986.Google Scholar
17.Levine, Marc and Morel, Fabien. Algebraic cobordism. Springer Monographs in Mathematics. Springer, Berlin, 2007.Google Scholar
18.Milnor, John. Algebraic K-theory and quadratic forms. Invent. Math. 9 (1969/1970), 318–344.Google Scholar
19.Morel, Fabien. Sur les puissances de l'idéal fondamental de l'anneau de Witt. Comment. Math. Helv. 79 (4) (2004), 689–703.Google Scholar
20.Morel, Fabien. -Algebraic Topology over a Field, Lecture Notes in Math. 2052 Springer, New York, 2012.CrossRefGoogle Scholar
21.Orlov, Dmitry, Vishik, Alexander, and Voevodsky, Vladimir. An exact sequence for KM*/2 with applications to quadratic forms. Ann. of Math. (2) 165 (1) (2007), 1–13.Google Scholar
22.Panin, Ivan. Oriented cohomology theories of algebraic varieties. K-Theory 30 (3) (2003), 265–314. Special issue in honor of Hyman Bass on his seventieth birthday. Part III.Google Scholar
23.Rost, Markus. Chow groups with coefficients. Doc. Math. 1 (16) (1996), 319–393 (electronic).Google Scholar
24.Totaro, Burt. Non-injectivity of the map from the Witt group of a variety to the Witt group of its function field. J. Inst. Math. Jussieu 2 (3) (2003), 483–493.CrossRefGoogle Scholar
25.Voevodsky, Vladimir. Motivic cohomology with Z=2-coefficients. Publ. Math. Inst. Hautes Études Sci. 98 (2003), 59–104.Google Scholar
26.Voevodsky, Vladimir. Reduced power operations in motivic cohomology. Publ. M ath. Inst. Hautes Études Sci. 98 (2003), 1–57.Google Scholar
27.Walter, Charles. Grothendieck-Witt groups of projective bundles. Preprint available at www.math.uiuc.edu/K-theory/0644/, 2003.Google Scholar