论文标题
椭圆形的椭圆形共同体，复的品种和衍生的等效性
Equivariant elliptic cohomology, toric varieties, and derived equivalences
论文作者
论文摘要
在本文中，我们研究了复杂的复杂品种的椭圆形共同体。我们证明了部分重建定理，表明椭圆形的椭圆形共同体编码有关曲奇品种x的e骨1骨骨骼的大量非平凡信息（尽管它停止了其GKM图的完全不变）。椭圆形的共同体应该编码更高的分类几何数据，并已提出将椭圆旋转与分类束相关的建议。特别是，与普通的共同体学和K理论相反，椭圆形的共同体预计不会成为代数品种的不变性。我们的第二个主要结果是通过证明存在与非同构椭圆形的椭圆形共同体相对的对等效品种成对来验证这一预测。
In this article we study the equivariant elliptic cohomology of complex toric varieties. We prove a partial reconstruction theorem showing that equivariant elliptic cohomology encodes considerable non-trivial information on the equivariant 1-skeleton of a toric variety X (although it stops short of being a complete invariant of its GKM graphs). Elliptic cohomology is supposed to encode higher categorical geometric data, and proposals have been made linking elliptic cocycles to categorified bundles. In particular, contrary to ordinary cohomology and K-theory, elliptic cohomology is expected not to be a derived invariant of algebraic varieties. Our second main result is to verify this prediction by showing that there exist pairs of equivariantly derived equivalent toric varieties with non-isomorphic equivariant elliptic cohomology.
