论文标题
理性$ T^2 $ Equivariant椭圆形的共同模型的代数模型
An algebraic model for rational $T^2$-equivariant elliptic cohomology
论文作者
论文摘要
我们构建了一个合理的$ t^2 $ - equivariant椭圆形的共同体学理论，该理论是从椭圆曲线C开始的，从椭圆曲线C开始，并围绕身份坐标数据。该理论是通过在代数模型类别中构建对象$ ec_ {t^2} $来定义的，$ da（t^2）$，Greenlees和Shipley与Rational $ T^2 $ -Spectra相当。该结果是对圆的构造[GRE05]的2道义的概括。对象$ ec_ {t^2} $是使用来自表面CXC结构捆的堂兄复合物的几何输入直接构建的。
We construct a rational $T^2$-equivariant elliptic cohomology theory for the 2-torus $T^2$, starting from an elliptic curve C over the complex numbers and a coordinate data around the identity. The theory is defined by constructing an object $EC_{T^2}$ in the algebraic model category $dA(T^2)$, which by Greenlees and Shipley is Quillen-equivalent to rational $T^2$-spectra. This result is a generalization to the 2-torus of the construction [Gre05] for the circle. The object $EC_{T^2}$ is directly built using geometric inputs coming from the Cousin complex of the structure sheaf of the surface CxC.
