arXiv subjects

Javier J. Gutiérrez

Publications and source records attributed to Javier J. Gutiérrez.

21 records · Page 2Linked to original sources

arXiv2010

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give suficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.

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arXiv2009

Dold-Kan correspondence for dendroidal abelian groups

We prove a Dold-Kan type correspondence between the category of dendroidal abelian groups and a suitably constructed category of dendroidal complexes. Our result naturally extends the classical Dold-Kan correspondence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes.

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arXiv2005

Homological localizations of Eilenberg-Mac Lane spectra

We discuss the Bousfield localization $L_E X$ for any spectrum $E$ and any $HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property of $HR$-modules, it is enough to study the localization of Eilenberg-Mac Lane spectra. Using general results about stable $f$-localizations, we give a method to compute the localization of an Eilenberg-Mac Lane spectrum $L_E HG$ for any spectrum $E$ and any abelian group $G$. We describe $L_E HG$ explicitly when $G$ is one of the following: finitely generated abelian groups, $p$-adic integers, Prüfer groups, and subrings of the rationals. The results depend basically on the $E$-acyclicity patterns of the spectrum $H\Q$ and the spectrum $H\Z/p$ for each prime $p$.

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