Blanc invariant conjecture for wrapped microlocal sheaf categories

Let QQ be a dd-dimensional Spinc\operatorname{Spin}^c manifold, let ΛTQ\Lambda\subset T^*Q be a conic Lagrangian, and let UQU\subset Q be open. Write ShΛw(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

ΣdK[TU,TUΛ]KBlanc(ShΛw(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 ShΛw(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.

Sources & referencesView supporting material

Primary source

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

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