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GL-algebras in positive characteristic I: the exterior algebra

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arxiv 2203.03693 v2 pith:D6VVVBOO submitted 2022-03-07 math.AC math.RT

Karthik Ganapathy This is my paper · ORCID
classification math.ACmath.RT
keywords algebracharacteristicexteriorpositiveboundcastelnuovo--mumfordcategorychurch--ellenberg
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We study the category of GL-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem a la Nagpal. Using this, we obtain a Church--Ellenberg type bound for the Castelnuovo--Mumford regularity. We also prove finiteness results for local cohomology.

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  1. GL-algebras in positive characteristic III: the divided power algebra

    math.AC 2026-08 conditional novelty 7.0 of 10

    The divided power algebra Div(k^∞) over a field of characteristic p is GL-coherent, and its bounded derived category of finitely presented modules has a semi-orthogonal decomposition into pieces generated by D^(r) ⊗ L_λ.

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