Blanc invariant conjecture for wrapped microlocal sheaf categories

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Let QQ be a dd-dimensional Spin⁡c\operatorname{Spin}^c manifold, let Λ⊂T∗Q\Lambda\subset T^*Q be a conic Lagrangian, and let U⊂QU\subset Q be open. Write Sh⁡Λw(U,C)⊂Sh⁡(U,C)\operatorname{Sh}_{\Lambda}^w(U,\mathbf{C})\subset\operatorname{Sh}(U,\mathbf{C}) for Nadler's wrapped category of sheaves with microsupport in Λ\Lambda. Blanc invariant conjecture. There is a natural map

Σ−dK[T∗U,T∗U−Λ]⟶KBlanc(Sh⁡Λw(U,C)),\Sigma^{-d}\mathbf{K}[T^*U,T^*U-\Lambda]\longrightarrow \mathbf{K}_{\mathrm{Blanc}}(\operatorname{Sh}_{\Lambda}^w(U,\mathbf{C})),

which is covariantly functorial for open embeddings, and whenever Sh⁡Λw(U,C)\operatorname{Sh}_{\Lambda}^w(U,\mathbf{C}) is homologically smooth and proper, this map is an isomorphism. This is proposed as an analogue of Ganatra's conjecture for exact manifolds; no resolution is supplied.

References

Primary source

David Treumann, “Complex K-theory of mirror pairs”, arXiv:1909.03018 (2019).

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