A Gersten-Witt spectral sequence for regular schemes
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 1, pp. 127-152.
@article{ASENS_2002_4_35_1_127_0,
     author = {Balmer, Paul and Walter, Charles},
     title = {A {Gersten-Witt} spectral sequence for regular schemes},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {127--152},
     publisher = {Elsevier},
     volume = {Ser. 4, 35},
     number = {1},
     year = {2002},
     doi = {10.1016/s0012-9593(01)01084-9},
     zbl = {1012.19003},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(01)01084-9/}
}
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
SP  - 127
EP  - 152
VL  - 35
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(01)01084-9/
DO  - 10.1016/s0012-9593(01)01084-9
LA  - en
ID  - ASENS_2002_4_35_1_127_0
ER  - 
%0 Journal Article
%A Balmer, Paul
%A Walter, Charles
%T A Gersten-Witt spectral sequence for regular schemes
%J Annales scientifiques de l'École Normale Supérieure
%D 2002
%P 127-152
%V 35
%N 1
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/s0012-9593(01)01084-9/
%R 10.1016/s0012-9593(01)01084-9
%G en
%F ASENS_2002_4_35_1_127_0
Balmer, Paul; Walter, Charles. A Gersten-Witt spectral sequence for regular schemes. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 35 (2002) no. 1, pp. 127-152. doi : 10.1016/s0012-9593(01)01084-9. http://archive.numdam.org/articles/10.1016/s0012-9593(01)01084-9/

[1] Balmer P., Derived Witt groups of a scheme, J. Pure Appl. Algebra 141 (1999) 101-129. | MR | Zbl

[2] Balmer P., Triangular Witt groups. Part I: The 12-term localization exact sequence, 19 (2000) 311-363. | MR | Zbl

[3] Balmer P., Triangular Witt groups. Part II: From usual to derived, Math. Z. 236 (2001) 351-382. | MR | Zbl

[4] Balmer P., Walter C., Derived Witt groups and Grothendieck duality, in preparation.

[5] Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, Astérisque 100 (1982). | MR | Zbl

[6] Cartan H., Eilenberg S., Homological Algebra, Princeton Univ. Press, 1956. | MR | Zbl

[7] Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, 1995. | MR | Zbl

[8] Ettner A., Zur Residuenabbildung in der Theorie quadratischer Formen, Diplomarbeit, Regensburg, 1999.

[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. | MR | Zbl

[10] Hartshorne R., Algebraic Geometry, Springer-Verlag, 1977. | MR | Zbl

[11] Keller B., On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1-56. | MR | Zbl

[12] Keller B., Appendix: On Gabriel-Roiter's axioms for exact categories, Trans. Amer. Math. Soc. 351 (1999) 677-681. | MR

[13] Mac Lane S., Categories for the Working Mathematician, Springer-Verlag, 1998. | MR | Zbl

[14] Milnor J., Husemoller D., Symmetric Bilinear Forms, Springer-Verlag, 1973. | MR | Zbl

[15] Neeman A., The derived category of an exact category, J. Algebra 135 (1990) 388-394. | MR | Zbl

[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. | MR | Zbl

[17] Ojanguren M., Panin I., A purity theorem for the Witt group, Ann. Scient. Éc. Norm. Sup. (4) 32 (1999) 71-86. | Numdam | MR | Zbl

[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. | MR | Zbl

[19] Pardon W., The filtered Gersten-Witt resolution for regular schemes, Preprint, 2000 , http://www.math.uiuc.edu/K-theory/0419/.

[20] Parimala R., Witt groups of affine three-folds, Duke Math. J. 57 (1988) 947-954. | MR | Zbl

[21] Quebbemann H.-G., Scharlau W., Schulte M., Quadratic and Hermitian forms in additive and Abelian categories, J. Algebra 59 (1979) 264-289. | MR | Zbl

[22] Ranicki A., Algebraic L-theory. I. Foundations, Proc. London Math. Soc. (3) 27 (1973) 101-125. | MR | Zbl

[23] Ranicki A., Additive L-theory, 3 (1989) 163-195. | MR | Zbl

[24] Rost M., http://www.math.ohio-state.edu/~rost/schmid.html.

[25] Schmid M., Wittringhomologie, Ph.D. dissertation, Regensburg 1997. Cf. [24].

[26] Verdier J.-L., Des catégories dérivées des catégories abéliennes (Thèse de doctorat d'état, Paris, 1967), Astérisque 239 (1996). | Numdam | MR | Zbl

[27] Walter C., Obstructions to the Existence of Symmetric Resolutions, in preparation.

[28] Weibel C., An Introduction to Homological Algebra, Cambridge Univ. Press, 1994. | MR | Zbl

Cité par Sources :