For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra \(A\mathbf{Ha}_C^0\) admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an \(A\mathbf{Ha}_C^0\)-action. These triples can be interpreted as certain sheaves on \(\mathbb {P}_C(\omega _C\oplus \mathcal {O}_C)\). In particular, we obtain an action of \(A\mathbf{Ha}_C^0\) on the cohomology of Hilbert schemes of points on \(T^*C\).

中文翻译：

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希格斯扭力滑轮的同调霍尔代数，三重模和滑轮的模量

对于任何自由定向的Borel-Moore同源理论A，我们在投影曲线C上的希格斯扭力绳轮叠堆的A理论上构造一个关联乘积。我们证明了所得的代数\（A \ mathbf {Ha} _C ^ 0 \）接受了自然的随机表示，并证明了当A替换为通常的Borel-Moore同源群时它是忠实的。我们还引入了稳定的三元组的模空间，这些空间受中岛箭袋品种的启发，后者的A-理论接受了\（A \ mathbf {Ha} _C ^ 0 \） -作用。这些三元组可以解释为\（\ mathbb {P} _C（\ omega _C \ oplus \ mathcal {O} _C）\）上的某些滑轮。特别地，我们对\（T ^ * C \）上的点的希尔伯特方案的同调性获得了\（A \ mathbf {Ha} _C ^ 0 \）的作用。