论文标题
希格斯捆绑包的模量复杂的K理论
Complex K-theory of moduli spaces of Higgs bundles
论文作者
论文摘要
我们建立了复杂$ k $的同构 - $ \ check $ \ check {\ mathcal {m}} $ $`sl_n“ $ - higgs $ d $ d $ and等级$ n $（在Hausel-thaddeus and the thaddeus）和Twisted Complect $ k $ - $ k $ - $ k $ - $ k $ - - $ \ hat {\ Mathcal {m}} $ $ pgl_n $ -higgs度$ e $，其中$（n，d）=（n，e）= 1 $，我们证明了$ h^*（\ check {\ Mathcal {\ Mathcal {\ Mathcal {M Mathcal {M Mathcal {M Mathcal {M Mathcal {\ Mathsed）$ - $ \ hat {\ Mathcal {M}} $。
We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold $\hat{\mathcal{M}}$ of $PGL_n$-Higgs bundles of degree $e$, where $(n,d)=(n,e)=1$. Along the way we prove the vanishing of torsion for $H^*(\check{\mathcal{M}})$ and certain twisted complex $K$-theory groups of $\hat{\mathcal{M}}$. We also extend Arinkin's autoduality of compactified Jacobian to a derived equivalence between $SL_n$ and $PGL_n$-Hitchin systems over the elliptic locus. In the appendix we develop a formalism of $G$-sheaves of spectra, generalising equivariant homotopy theory to a relative setting.
