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Non-noetherian GL-algebras in characteristic two

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arxiv 2408.04630 v2 pith:ZWIQWXL7 submitted 2024-08-08 math.AC math.COmath.RT

Karthik Ganapathy This is my paper · ORCID
classification math.ACmath.COmath.RT
keywords characteristicinfinitenon-noetherianareaascendingbuildchainconstruct
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Over fields of characteristic two, we construct an infinite ascending chain of GL-stable ideals in the coordinate ring of infinite skew-symmetric matrices. This construction provides the first known example of a non-noetherian GL-algebra, thereby resolving a long-standing open question in the area. Our results build on the work of Draisma, Krasilnikov, and Krone.

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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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