A.S. Sivatski: Applications of Conics to Certain Quadratic Forms over the Rational Function Fields


Submission: 2010, Dec 26

A few results on quadratic forms over fields are obtained. In particular, we show that for any forms $\phi_1$ and $\phi_2$ over a field $k$ of characteristic different from $2$ and $a\in k^*$, the anisotropic part of the form $\phi_1\perp (t^2-a)\phi_2$ over the rational function field $k(t)$ is of the same type, i.e. there exist forms $\tau_1$ and $\tau_2$ over $k$ such that $\phit_{an}\simeq\taut$. Also we determine the structure of certain Pfister forms over $k(t)$, and describe the behavior of quadratic forms under biquadratic extensions of $k$ in terms of some related forms over the function field of the product of two conics over $k(x)$, or $k(x,y)$.

2010 Mathematics Subject Classification:

Keywords and Phrases:

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