论文标题
光滑的小组，ii：令人振奋的模式
Smooth profinite groups, II: the Uplifting Pattern
论文作者
论文摘要
本文介绍了平滑的涂鸦基和环形成对理论的方案理论，该理论是在论文“平滑的涂鸦基团，i”中引入的。为此，我们的主要技术工具是Hochschild offine group方案的共同学和提升矢量束的Frobenius。这项工作的主要贡献是令人振奋的模式。这是一个自然的过程，将矢量捆绑包的给定等效扩展提升到其$ \ MATHBF W_2 $ -COUNTERPART，以“合理”的基础变化和群体变换的“合理”组合。这是证明平滑度定理的关键要素，在纸上“光滑的涂鸦基团”中。
This text presents a scheme-theoretic enhancement of the theory of smooth profinite groups and cyclotomic pairs, introduced in the paper `Smooth profinite groups, I'. To do so, our main technical tools are Hochschild cohomology of affine group schemes and lifting frobenius of vector bundles. The main contribution of this work is the Uplifting Pattern. It is a natural process, to lift a given equivariant extension of vector bundles, to its $\mathbf W_2$-counterpart, upon a `reasonable' combination of base-change and group-change. This is the key ingredient to prove the Smoothness Theorem, in the paper `Smooth profinite groups, III'.
