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 AHaC0 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 AHaC0-action. These triples can be interpreted as certain sheaves on PC(omega C circle plus OC). In particular, we obtain an action of AHaC0 on the cohomology of Hilbert schemes of points on T*C.
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机译:对于任何免费的Borel-Moore同源理论a,我们构建了一个关联产品,在突起的曲线C上构建了一堆Higgs扭转滑轮的理论。我们表明所得到的代数AHAC0承认自然的洗牌呈现,并证明它 当A替换为常规的Borel-Moore同源群时,忠诚。 我们还介绍了稳定三分之一的Moduli空间,受到Nakajima Quiver品种的严重启发,其一个理论承认AHAC0行动。 这些三元组可以被解释为PC上的某些滑轮(Omega C Circle Plus OC)。 特别是,我们获得AHAC0对T * C的点数的同学的作用。
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