Cohomological Hall algebra of Higgs sheaves on a curve
Cohomological Hall algebra of Higgs sheaves on a curve
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DOI：
10.14231/ag-2020-010
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发表时间：
2018-01
影响因子：
1.5
通讯作者：
Francesco Sala;O. Schiffmann
中科院分区：
文献类型：
--
作者：
Francesco Sala;O. Schiffmann
在任意取向Borel-Moore同调理论的背景下，我们定义了光滑投影曲线X上的（2维）CalabiYau范畴的Higgs捆的上同霍尔代数AHAHiggs(X)，以及它的幂零和半稳定变体。在通常的Borel-Moore同调情况下，AHAHiggs(X)是X上相干束堆的（泛）上同调环H上的一个模。我们将其湮灭子表征为H模，并提供了一个显式的生成子集合（映射Higgsr， d→Cohr， d的零截面的基类集合[Cohr， d]，对于r >0, d∈Z, r = 0, d∈Z>0）。Salimmo sù， el primo e IO second, tanto ' s ' vidi ' de le le belle che porta ' l ciel, per UN pertugio tondo。但丁，《神圣喜剧》，地狱篇，第三十四章
We define the cohomological Hall algebra AHAHiggs(X) of the (2-dimensional) CalabiYau category of Higgs sheaves on a smooth projective curve X, as well as its nilpotent and semistable variants, in the context of an arbitrary oriented Borel-Moore homology theory. In the case of usual Borel-Moore homology, AHAHiggs(X) is a module over the (universal) cohomology ring H of the stacks of coherent sheaves on X. We characterize its annihilator as a H-module, and we provide an explicit collection of generators (the collection of fundamental classes [Cohr, d ] of the zero-sections of the maps Higgsr, d → Cohr, d , for r > 0, d ∈ Z and r = 0 and d ∈ Z>0). salimmo sù, el primo e io secondo, tanto ch’i’ vidi de le cose belle che porta ’l ciel, per un pertugio tondo. Dante Alighieri, la Divina Commedia, Inferno, Canto XXXIV