论文标题
关于衍生的碎片的某些特性
On some properties of birational derived splinters
论文作者
论文摘要
如果所有适当的Birational Maps $ x \ to \ operatatorName {spec}（a）$，noetherian降低的环$ a $称为Birational派生的碎片，则称为$ x \ to rf _*\ Mathcal {o} _x $ splits。在同等的特征零中，此属性的特征是理性的概念，但是在积极或混合的特征中可以说的要少得多。在本文中，我们证明了这一概念的一些基本属性，包括本地化的行为，采取纯粹的子序，直接限制并沿着典型的扩展。特别是，特征零的理性概念的直接极限具有合理的概念。然后，我们研究了残留的扩展（任意特征），以及正常特征的开放性和定期扩展，与datta-tucker平行以及作者先前关于碎片的作品。
A Noetherian reduced ring $A$ is called a birational derived splinter if for all proper birational maps $X\to\operatorname{Spec}(A)$, the canonical map $A\to Rf_*\mathcal{O}_X$ splits. In equal characteristic zero this property characterizes rational singularities, but much less can be said in positive or mixed characteristics. In this paper, we prove some fundamental properties of this notion, including the behavior under localization, taking a pure subring, taking direct limit, and along an étale extension. In particular, direct limit of rational singularities in characteristic zero has rational singularities. Then, we study residue extensions (in arbitrary characteristic), and openness and regular extensions in positive characteristic, parallel to Datta-Tucker and the author's previous works on splinters.
