Equivariant Hodge theory and noncommutative geometry
Equivariant Hodge theory and noncommutative geometry
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DOI：
10.2140/gt.2020.24.2361
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发表时间：
2015-07
影响因子：
2
通讯作者：
Daniel Halpern-Leistner;Daniel Pomerleano
中科院分区：
文献类型：
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作者：
Daniel Halpern-Leistner;Daniel Pomerleano
我们发展了一类光滑上同真商堆$X/G$的Hodge理论，类似于光滑投影格式的Hodge理论。证明了等变相干轴类的非交换Hodge-de Rham序列的退化性。这个谱序列收敛于周期循环同调，我们用X$关于极大紧子群$M \子集G$的拓扑等变$K$理论对它进行了规范的等价。结果是一个权重$n$在$K^n_M(X^{an})$上的自然的纯Hodge结构。我们也处理了等变朗多-金兹堡模型的矩阵分解范畴。
We develop a version of Hodge theory for a large class of smooth cohomologically proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge-de Rham sequence for the category of equivariant coherent sheaves degenerates. This spectral sequence converges to the periodic cyclic homology, which we canonically identify with the topological equivariant $K$-theory of $X$ with respect to a maximal compact subgroup $M \subset G$. The result is a natural pure Hodge structure of weight $n$ on $K^n_M(X^{an})$. We also treat categories of matrix factorizations for equivariant Landau-Ginzburg models.