链式引理，二次型和符号长度

Pub Date : 2023-09-30 DOI:10.36045/j.bbms.230123

Adam Chapman, Ilan Levin

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引用次数: 0

摘要

我们想要限定${_{2^{m-1}}Br}(F)$中由$2^m$次的5或6个循环代数的张量积表示的类的符号长度。其主要成分是二次型的链式引理，广义Clifford不变量的一种形式，以及fister和Rost在I^ 3f $中对12维和14维形式的描述。

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Chain Lemma, Quadratic Forms and Symbol Length

We want to bound the symbol length of classes in ${_{2^{m-1}}Br}(F)$ which are represented by tensor products of 5 or 6 cyclic algebras of degree $2^m$. The main ingredients are the chain lemma for quadratic forms, a form of a generalized Clifford invariant and Pfister's and Rost's descriptions of 12- and 14-dimensional forms in $I^3 F$.

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