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Castelnuovo-Mumford regularity up to symmetry

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arxiv 1806.00457 v3 pith:SLXZP2IQ submitted 2018-06-01 math.AC

Dinh Van Le , Uwe Nagel , Hop D. Nguyen , Tim Roemer This is my paper · ORCID
classification math.AC
keywords regularityidealscastelnuovo-mumfordconjectureactionalongartinianasymptotic
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We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.

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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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