论文标题
派生的代数谱率
Derived Algebraic Cobordism
论文作者
论文摘要
我们构建并研究了衍生方案的双变量恢复理论。我们的理论提供了对特征性0代数方案的代数界界理论的广泛概括，该方案由莱文和莫雷尔（Levine and Morel）早期构建，以及一个（部分）非 - $ \ ab^1 $ invariant的动机共同体学$ mgl $ MGL $ MGL $ MOREL-VOEVODSKY的稳定动机的动机理论。我们的主要结果是，双变量的恢复能力满足投影捆绑的公式。作为此的应用，我们构建了COBORDISM CHERN类别的向量束，并建立了Coobordism Cromology环与矢量束的Grothendieck环之间建立牢固的联系。我们还为我们的理论提供了几种通用属性。此外，我们的代数恢复也被用来构建难以捉摸的方案共同学理论的候选者。
We construct and study a theory of bivariant cobordism of derived schemes. Our theory provides a vast generalization of the algebraic bordism theory of characteristic 0 algebraic schemes, constructed earlier by Levine and Morel, and a (partial) non-$\Ab^1$-invariant refinement of the motivic cohomology theory $MGL$ in Morel--Voevodsky's stable motivic homotopy theory. Our main result is that bivariant cobordism satisfies the projective bundle formula. As applications of this, we construct cobordism Chern classes of vector bundles, and establish a strong connection between the cobordism cohomology rings and the Grothendieck ring of vector bundles. We also provide several universal properties for our theory. Additionally, our algebraic cobordism is also used to construct a candidate for the elusive theory of Chow cohomology of schemes.
