Graded Witt ring and unramified cohomology |
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Authors: | R. Parimala and R. Sridharan |
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Affiliation: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabba Road, 400 005 Bombay, India |
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Abstract: | It is proved that for a smooth affine curveX over a local ring or global field, the graded Witt ring ofX is isomorphic to the graded unramified cohomology ring ofX. IfX is projective and has a rational point, the same result holds if and only if every quadratic space defined on the complement of a rational point extends toX. Such an extension is possible, for instance, if the canonical line bundle onX is a square in PicX. |
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Keywords: | Witt ring unramified é tale cohomology signature real spectrum cohomological dimension |
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