论文标题
前代主义和恢复主义
Precobordism and cobordism
论文作者
论文摘要
本文的目的是比较作者和其他人先前构建的几个版本的Bivariant代数Coobordism。 In particular, we show that a simple construction based on the universal precobordism theory of Annala--Yokura agrees with the more complicated theory of bivariant derived algebraic cobordism constructed earlier by the author, and that both of these theories admit a Grothendieck transformation to operational cobordism constructed by Luis González--Karu over fields of characteristic 0. The proofs are partly based on convenient universal对几种恢复理论的特征，应该具有独立的利益。使用类似的技术，我们还加强了Vezzosi在运营派生的$ K $理论中的结果。在附录中，我们在代数界群中详细构建了虚拟回调的详细构造，从而填补了Lowrey-Schürg的构建空白。
The purpose of this article is to compare several versions of bivariant algebraic cobordism constructed previously by the author and others. In particular, we show that a simple construction based on the universal precobordism theory of Annala--Yokura agrees with the more complicated theory of bivariant derived algebraic cobordism constructed earlier by the author, and that both of these theories admit a Grothendieck transformation to operational cobordism constructed by Luis González--Karu over fields of characteristic 0. The proofs are partly based on convenient universal characterizations of several cobordism theories, which should be of independent interest. Using similar techniques, we also strengthen a result of Vezzosi on operational derived $K$-theory. In the appendix, we give a detailed construction of virtual pullbacks in algebraic bordism, filling the gaps in the construction of Lowrey--Schürg.
