Holomorphic Frobenius Actions for DQ-Modules

  • François Petit

    University of Luxembourg, Esch-sur-Alzette, Luxembourg
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Given a complex manifold endowed with a -action and a DQ-algebra equipped with a compatible holomorphic Frobenius action (F-action), we prove that if the -action is free and proper, then the category of F-equivariant DQ-modules is equivalent to the category of modules over the sheaf of invariant sections of the DQ-algebra. As an application, we deduce the codimension-three conjecture for formal microdifferential modules from the one for DQ-modules on a symplectic manifold.

Cite this article

François Petit, Holomorphic Frobenius Actions for DQ-Modules. Publ. Res. Inst. Math. Sci. 58 (2022), no. 1, pp. 187–226

DOI 10.4171/PRIMS/58-1-5