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Pré-Publication, Document De Travail Année : 2022

Homotopy theory of spectral sequences

Résumé

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page. We show that this admits a structure close to that of a category of fibrant objects in the sense of Brown and in particular the structure of a partial Brown category with fibrant objects. We use this to compare with related structures on the categories of multicomplexes and filtered complexes.

Dates et versions

hal-03834361 , version 1 (29-10-2022)

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Muriel Livernet, Sarah Whitehouse. Homotopy theory of spectral sequences. 2022. ⟨hal-03834361⟩
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