# On the Witt rings of function fields of quasihomogeneous varieties

Colloquium Mathematicae (1997)

- Volume: 73, Issue: 2, page 195-219
- ISSN: 0010-1354

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topJaworski, Piotr. "On the Witt rings of function fields of quasihomogeneous varieties." Colloquium Mathematicae 73.2 (1997): 195-219. <http://eudml.org/doc/210486>.

@article{Jaworski1997,

author = {Jaworski, Piotr},

journal = {Colloquium Mathematicae},

keywords = {Witt rings; graded rings; selfdual vector bundles; quasihomogeneous varieties; residue homomorphisms; Witt ring; valuation; residue homomorphism; graded ring; quasihomogeneous variety},

language = {eng},

number = {2},

pages = {195-219},

title = {On the Witt rings of function fields of quasihomogeneous varieties},

url = {http://eudml.org/doc/210486},

volume = {73},

year = {1997},

}

TY - JOUR

AU - Jaworski, Piotr

TI - On the Witt rings of function fields of quasihomogeneous varieties

JO - Colloquium Mathematicae

PY - 1997

VL - 73

IS - 2

SP - 195

EP - 219

LA - eng

KW - Witt rings; graded rings; selfdual vector bundles; quasihomogeneous varieties; residue homomorphisms; Witt ring; valuation; residue homomorphism; graded ring; quasihomogeneous variety

UR - http://eudml.org/doc/210486

ER -

## References

top- [1] N. Bourbaki, Commutative Algebra, Hermann, 1972.
- [2] F. Fernández-Carmena, 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. Zbl0641.14003
- [3] R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977.
- [4] P. Jaworski, About the Witt rings of function fields of algebroid quadratic quasihomogeneous surfaces, Math. Z. 218 (1995), 319-342. Zbl0827.13010
- [5] P. Jaworski, About the Milnor's K-theory of function fields of quasihomogeneous cones, K-Theory 10 (1996), 83-105. Zbl0844.19003
- [6] M. Knebusch, Symmetric bilinear forms over algebraic varieties, in: Conference on Quadratic Forms (Kingston 1976), Queen's Papers in Pure and Appl. Math. 46 1977, 102-283.
- [7] T. Y. Lam, Algebraic Theory of Quadratic Forms, Benjamin, Reading, Mass., 1973.
- [8] J. Milnor and D. Husemoller, Symmetric Bilinear Forms, Springer, Berlin, 1973.
- [9] M. Ojanguren, The Witt Group and the Problem of Lüroth, ETS Editrice Pisa, 1990.
- [10] W. Pardon, A relation between Witt group of a regular local ring and the Witt groups of its residue class fields, preprint.
- [11] W. Scharlau, Quadratic and Hermitian Forms, Springer, Berlin, 1985. Zbl0584.10010
- [12] P. Wagreich, The structure of quasihomogeneous singularities, in: Singularities, Proc. Sympos. Pure Math. 40, Amer. Math. Soc., 1983, 593-611. Zbl0545.14028

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