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3 results

A note on the Witt group and the KO-theory of complex Grassmannians
Nobuaki Yagita
Journal:

Journal of K-Theory / Volume 9 / Issue 1 / February 2012

Published online by Cambridge University Press:

22 March 2011, pp. 161-175

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February 2012
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For a complex Grassmannian X, there is an isomorphism
between Balmer's Witt group and the quotient of topological K-theories.

Koszul complexes and symmetric forms over the punctured affine space
Paul Balmer, Stefan Gille
Journal:

Proceedings of the London Mathematical Society / Volume 91 / Issue 2 / September 2005

Published online by Cambridge University Press:

23 August 2005, pp. 273-299

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September 2005
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Let $X$ be a regular separated scheme of finite Krull dimension and let $U^{n}_{X} \subset A^{n}_{X}$ be the punctured affine $n$-space over $X$. We show that the total graded Witt ring of $U^{n}_{X}$ is a free graded module over the total graded Witt ring of $X$ with two generators $1$ and $\epsilon$. The second generator satisfies the equation $\epsilon^{2} = 1$ when $n = 1$ and $\epsilon^{2} = 0$ when $n \geq 2$.

NON-INJECTIVITY OF THE MAP FROM THE WITT GROUP OF A VARIETY TO THE WITT GROUP OF ITS FUNCTION FIELD
Burt Totaro
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 2 / Issue 3 / July 2003

Published online by Cambridge University Press:

21 July 2003, pp. 483-493

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July 2003
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We exhibit a smooth complex affine 5-fold whose Witt group of quadratic forms does not inject into the Witt group of its function field. The dimension 5 is the smallest possible. The example depends on relating Witt groups, mod 2 Chow groups, and Steenrod operations.
AMS 2000 Mathematics subject classification: Primary 19G12. Secondary 19E15

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3 results

A note on the Witt group and the KO-theory of complex Grassmannians

Koszul complexes and symmetric forms over the punctured affine space

NON-INJECTIVITY OF THE MAP FROM THE WITT GROUP OF A VARIETY TO THE WITT GROUP OF ITS FUNCTION FIELD