论文标题
TOR光谱序列和平坦的形态在同位素$ D $几何形式中
The Tor Spectral Sequence and Flat Morphisms in Homotopical $D$-Geometry
论文作者
论文摘要
同位代数$ D $ - 几何结合了Toen和Vezzosi的同位代数几何以及贝利森和德林菲尔德的几何形状的各个方面。该论文的最后两位作者和Di Brino引入了它，是对Batalin-Vilkovisky复合物进行无坐标研究的合适框架，更普遍地用于研究非线性部分偏微分方程及其对称性。为了巩固该理论的基础，我们必须证明，线性和交换代数的标准方法可以在同义代数$ d $ - 几何的背景下获得，并且我们必须证明，在这种情况下，étale拓扑是一种同质的态度，是一种同质的态度和平稳的态度。这项工作的前半部分完成了。其余部分涵盖了对划分$ d $ algebras的类别中的典型和扁平形态的研究，并基于Tor光谱序列，该光谱序列将同源性的分级TOR函数与两个差异分级$ D $ D $ -Modules的衍生张量产物的同源性连接起来，而不是差异$ d $ d $ -D $ -Alge-d $ -Algebra。
Homotopical algebraic $D$-geometry combines aspects of homotopical algebraic geometry of Toen and Vezzosi and $D$-geometry of Beilinson and Drinfeld. It was introduced by the paper's last two authors and di Brino as a suitable framework for a coordinate-free study of the Batalin-Vilkovisky complex and more generally for the study of non-linear partial differential equations and their symmetries. In order to consolidate the foundation of the theory, we have to prove that the standard methods of linear and commutative algebra are available in the context of homotopical algebraic $D$-geometry, and we must show that in this context the étale topology is a kind of homotopical Grothendieck topology and that the notion of smooth morphism is, roughly speaking, local for the étale topology. The first half of this work was done. The remaining part covers the study of étale and flat morphisms in the category of differential graded $D$-algebras and is based on the Tor spectral sequence which connects the graded Tor functors in homology with the homology of the derived tensor product of two differential graded $D$-modules over a differential graded $D$-algebra.
