论文标题
基本独立代数
Base independent algebraic cobordism
论文作者
论文摘要
本文的目的是表明，作者先前考虑的Bivariant代数$ a $ a-cobordism群体独立于所选的基本环$ a $。通过分析所谓的SNC关系产生的双变量理想来证明这一结果，尽管我们为此理想获得的替代表征本身是有趣的，因为它的简单性，也许更重要的是，它使我们能够轻松地扩展双分数代数的Coobordism，以扩展到有限的Krull Dimenties Krull Dimension divisorian衍生的Noetherian衍生的方案。作为一个有趣的推论，我们定义了称为代数bordism的相应同源理论。我们还概括了投射捆绑式公式，Chern类的理论，Conner-Floyd Theorem和Grothendieck--Riemann-Roch Theorem。双变量恢复主义的一般定义是基于对Noetherian衍生方案的充分线条束和准标记形态的仔细研究，这也是在这项工作中进行的。
The purpose of this article is to show that the bivariant algebraic $A$-cobordism groups considered previously by the author are independent of the chosen base ring $A$. This result is proven by analyzing the bivariant ideal generated by the so called snc relations, and, while the alternative characterization we obtain for this ideal is interesting by itself because of its simplicity, perhaps more importantly it allows us to easily extend the definition of bivariant algebraic cobordism to divisorial Noetherian derived schemes of finite Krull dimension. As an interesting corollary, we define the corresponding homology theory called algebraic bordism. We also generalize projective bundle formula, the theory of Chern classes, the Conner--Floyd theorem and the Grothendieck--Riemann--Roch theorem to this setting. The general definitions of bivariant cobordism is based on the careful study of ample line bundles and quasi-projective morphisms of Noetherian derived schemes, also undertaken in this work.
