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On finiteness properties of polynomial functors

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arxiv 1308.4698 v6 pith:VXSMV75X submitted 2013-08-21 math.AT math.CTmath.RT

Aurélien Djament (LMJL) This is my paper · ORCID
classification math.ATmath.CTmath.RT
keywords functorscategoryfinitenesspolynomialpropertiesabelianapplicationarchives-ouvertes
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We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors from a small symmetric monoidal category whose unit is an initial object to an abelian category (notion introduced in this general setting in the work http://hal.archives-ouvertes.fr/hal-00851869 joint with C. Vespa). We give also an application to functors related to automorphisms of free groups.

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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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