A Gersten–Witt spectral sequence for regular schemes

Paul Balmer; Charles Walter

Annales scientifiques de l'École Normale Supérieure (2002)

  • Volume: 35, Issue: 1, page 127-152
  • ISSN: 0012-9593

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Balmer, Paul, and Walter, Charles. "A Gersten–Witt spectral sequence for regular schemes." Annales scientifiques de l'École Normale Supérieure 35.1 (2002): 127-152. <http://eudml.org/doc/82563>.

@article{Balmer2002,
author = {Balmer, Paul, Walter, Charles},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Witt groups of regular schemes; Gersten-Witt complex; Gersten-Witt spectral sequence; purity},
language = {eng},
number = {1},
pages = {127-152},
publisher = {Elsevier},
title = {A Gersten–Witt spectral sequence for regular schemes},
url = {http://eudml.org/doc/82563},
volume = {35},
year = {2002},
}

TY - JOUR
AU - Balmer, Paul
AU - Walter, Charles
TI - A Gersten–Witt spectral sequence for regular schemes
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2002
PB - Elsevier
VL - 35
IS - 1
SP - 127
EP - 152
LA - eng
KW - Witt groups of regular schemes; Gersten-Witt complex; Gersten-Witt spectral sequence; purity
UR - http://eudml.org/doc/82563
ER -

References

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  1. [1] Balmer P., Derived Witt groups of a scheme, J. Pure Appl. Algebra141 (1999) 101-129. Zbl0972.18006MR1706376
  2. [2] Balmer P., Triangular Witt groups. Part I: The 12-term localization exact sequence, 19 (2000) 311-363. Zbl0953.18003MR1763933
  3. [3] Balmer P., Triangular Witt groups. Part II: From usual to derived, Math. Z.236 (2001) 351-382. Zbl1004.18010MR1815833
  4. [4] Balmer P., Walter C., Derived Witt groups and Grothendieck duality, in preparation. 
  5. [5] Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, Astérisque100 (1982). Zbl0536.14011MR751966
  6. [6] Cartan H., Eilenberg S., Homological Algebra, Princeton Univ. Press, 1956. Zbl0075.24305MR77480
  7. [7] Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, 1995. Zbl0819.13001MR1322960
  8. [8] Ettner A., Zur Residuenabbildung in der Theorie quadratischer Formen, Diplomarbeit, Regensburg, 1999. 
  9. [9] Fernández-Carmena F., On the injectivity of the map of the Witt group of a scheme into the Witt group of its function field, Math. Ann.277 (1987) 453-468. Zbl0641.14003MR891586
  10. [10] Hartshorne R., Algebraic Geometry, Springer-Verlag, 1977. Zbl0367.14001MR463157
  11. [11] Keller B., On the cyclic homology of exact categories, J. Pure Appl. Algebra136 (1999) 1-56. Zbl0923.19004MR1667558
  12. [12] Keller B., Appendix: On Gabriel–Roiter's axioms for exact categories, Trans. Amer. Math. Soc.351 (1999) 677-681. MR1608305
  13. [13] Mac Lane S., Categories for the Working Mathematician, Springer-Verlag, 1998. Zbl0906.18001MR354798
  14. [14] Milnor J., Husemoller D., Symmetric Bilinear Forms, Springer-Verlag, 1973. Zbl0292.10016MR506372
  15. [15] Neeman A., The derived category of an exact category, J. Algebra135 (1990) 388-394. Zbl0753.18004MR1080854
  16. [16] Ojanguren M., Parimala R., Sridharan R., Suresh V., Witt groups of the punctured spectrum of a 3-dimensional local ring and a purity theorem, J. London Math. Soc.59 (1999) 521-540. Zbl0930.19003MR1709663
  17. [17] Ojanguren M., Panin I., A purity theorem for the Witt group, Ann. Scient. Éc. Norm. Sup. (4)32 (1999) 71-86. Zbl0980.11025MR1670591
  18. [18] Pardon W., A relation between Witt groups and 0-cycles in a regular ring, in: Springer Lect. Notes Math., 1046, 1984, pp. 261-328. Zbl0531.10024MR750687
  19. [19] Pardon W., The filtered Gersten–Witt resolution for regular schemes, Preprint, 2000 , http://www.math.uiuc.edu/K-theory/0419/. 
  20. [20] Parimala R., Witt groups of affine three-folds, Duke Math. J.57 (1988) 947-954. Zbl0674.14029MR975129
  21. [21] Quebbemann H.-G., Scharlau W., Schulte M., Quadratic and Hermitian forms in additive and Abelian categories, J. Algebra59 (1979) 264-289. Zbl0412.18016MR543249
  22. [22] Ranicki A., Algebraic L-theory. I. Foundations, Proc. London Math. Soc. (3)27 (1973) 101-125. Zbl0269.18009MR414661
  23. [23] Ranicki A., Additive L-theory, 3 (1989) 163-195. Zbl0686.57017MR1029957
  24. [24] Rost M., http://www.math.ohio-state.edu/~rost/schmid.html. 
  25. [25] Schmid M., Wittringhomologie, Ph.D. dissertation, Regensburg 1997. Cf. [24]. 
  26. [26] Verdier J.-L., Des catégories dérivées des catégories abéliennes (Thèse de doctorat d'état, Paris, 1967), Astérisque239 (1996). Zbl0882.18010MR1453167
  27. [27] Walter C., Obstructions to the Existence of Symmetric Resolutions, in preparation. 
  28. [28] Weibel C., An Introduction to Homological Algebra, Cambridge Univ. Press, 1994. Zbl0797.18001MR1269324

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