关于Berkovich双重剩余域与双有理模型
On the Berkovich double residue fields and birational models
AI总结：
本文定义了Berkovich解析空间点的双重剩余域，将其等同于双有理模型中中心剩余域的并集，并具体计算了拟单项赋值的该域。
摘要：
正如代数簇上的一点可以定义剩余域一样，我们也可以对Berkovich解析空间中的一点考虑其剩余域。该剩余域在代数意义下是一个赋值域。然后我们可以将其剩余域再次视为赋值域，称之为该点处的Berkovich双重剩余域。在本文中，我们考虑代数簇的Berkovich解析化中的一点$x$，并将$x$处的Berkovich双重剩余域等同于$x$在双有理模型中的中心处的剩余域的并集。此外，我们具体计算了任意拟单项赋值的Berkovich双重剩余域。
英文摘要：
Just as a residue field can be considered for a point of an algebraic variety, we can also consider a residue field for a point of a Berkovich analytic space. This residue field is a valuation field in the algebraic sense. Then we can consider its residue field as a valuation field. We call it the Berkovich double residue field at the point. In this paper, we consider a point $x$ of the Berkovich analytification of an algebraic variety and identify the Berkovich double residue field at $x$ with the union of the residue fields at the center of $x$ in birational models. Besides, we concretely compute the Berkovich double residue field for any quasi monomial valuation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
