Noncommutative resolution, F-blowups and D-modules

Abstract

We explain the isomorphism between the $G$-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of $D$-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.

14 pages, v.2: to appear in Adv. Math

References in corpus (2)

• Universal flattening of Frobenius
• On monotonicity of F-blowup sequences

Cited by in corpus (7)

• Universal flattening of Frobenius
• On monotonicity of F-blowup sequences
• F-blowups of normal surface singularities
• Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms
• Frobenius morphisms of noncommutative blowups
• Non-commutative resolutions of linearly reductive quotient singularities
• Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures