K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \pm 1

Details K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \pm 1 K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \pm 1

2010-10-28

arxiv.org/abs/1010.5880v1

Mathematics

K-Theory and Homology

Scientific paper

Let $k$ be a field of characteristic $\ne 2$ and let $Q_{n,m}(x_1,
...,x_n,y_1, ...,y_m)=x_1^2+ ... +x_n^2-(y_1^2+ ... +y_m^2)$ be a quadratic
form over $k$. Let $R(Q_{n,m})=R_{n,m}=k[x_1, ...,x_n,y_1,
...,y_m]/(Q_{n,m}-1)$. In this note we will calculate $\wt K_0(R_{n,m})$ for
every $n,m \geq 0$.

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