R. Aravire and R. Baeza: Linkage of fields in characteristic 2

rbaeza@inst-mat.utalca.cl

Submission: 2001, Nov 6

Let $F$ be a field with $2=0$ and $\varphi=\ll a_1,\ldots,a_n\gg$ an $n$-fold anisotropic bilinear Pfister form over $F$ with function field $F(\varphi)$. In this paper we compute $\ker[I^n_F/I^{n+1}_F\rightarrow I^n_{F(\varphi)}/I^{n+1}_{F(\varphi)}]$ where $I_F\subset W(F)$ is the maximal ideal in the Witt ring $W(F)$ of $F$. We use this computation to prove a $n$-linkage property of the subfields $F^2(a_1,\ldots,a_n)$.

2000 Mathematics Subject Classification: 11E04, 11E81, 12E05

Keywords and Phrases: bilinear-, quadratic-, differential forms, Witt rings.

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