论文标题
特征p和双线性形式的差分形式的功能场扩展和特征2中的双线性形式2
Function field extensions and annihilators of differential forms in characteristic p and bilinear forms in characteristic 2
论文作者
论文摘要
令$ f $为特征$ p> 0 $的字段，让$ω^n（f）$是$ n $ differenten-differenten forms of $ f $的$ f $ - 向量空间。在这项工作中，我们将研究$ p $ - forms的迭代函数字段扩展的$ω^n（f）$的行为。我们将使用以前的工作中的结果将限制性映射的内核重写$ω^n（f）\ toω^n（f（φ_1，\ ldots，φ_r））$将其纳入一组由$φ_1，\ ldots的规范字段给出的特定形式的差异形式。我们将通过将新的重新剥落转换为特征性$ 2 $的领域的双线性形式的理论来结束这项工作。
Let $F$ be a field of characteristic $p>0$ and let $Ω^n(F)$ be the $F$-vector space of $n$-differential forms over $F$. In this work we will study the behaviour of $Ω^n(F)$ under iterated function field extensions of $p$-forms. We will use results from a previous work to rewrite the kernel of the restriction map $Ω^n(F) \to Ω^n(F(φ_1,\ldots,φ_r))$ to a set of differential forms annihilated by specific forms given by the norm fields of $φ_1,\ldots,φ_r$. We will close this work by translating the new resluts to the theory of bilinear forms over fields of characteristic $2$.
