Nil-localization of unstable algebras over the Steenrod algebra
type: Item
instance of: scholarly article
title: Nil-localization of unstable algebras over the Steenrod algebra
zbMATH Open document ID: 0639.55012
DOI: 10.1007/BF01161641
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173984
review text: Let p be an odd prime, \(A\) \(*_ p\) the mod p Steenrod algebra, K the category of unstable \(A\) \(*_ p\)-algebras and K' the full subcategory of K of those algebras which are concentrated in even degrees. We say that an unstable \(A\) \(*_ p\)-algebra is Nil-closed if the underlying \(A\) \(*_ p\)-module is Nil-closed in the sense of \textit{J. Lannes} and the second author [Ann. Sci. Éc. Norm. Sup. IV, Sér. 19, 303-333 (1986; Zbl 0608.18006), 6.2.1]. In the first part of the note we introduce the concept of Nil- localization of unstable \(A\) \(*_ p\)-algebras and we prove: Theorem. For any unstable \(A\) \(*_ p\)-algebra K, there exists a unique (up to isomorphism) nil-closed unstable \(A\) \(*_ p\)-algebra, denoted \(N_ K^{-1}(K)\), and a natural map of \(A\) \(*_ p\)-algebras \(\mu _ K: K\to N_ K^{-1}(K)\) which is initial among maps of unstable \(A\) \(*_ p\)- algebras from K to nil-closed unstable \(A\) \(*_ p\)-algebras. In the second part we show that some results of Adams-Wilkerson and of Rector, which occur in K' can be extended to K. This allows us to determine the Nil-localization of certain unstable \(A\) \(*_ p\)-algebras.
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 4042848
zbMATH Keywords: mod p Steenrod algebra
zbMATH Keywords: category of unstable algebras over the Steenrod algebra
zbMATH Keywords: Nil-closed
zbMATH Keywords: Nil-localization of unstable algebras
author: Carles Broto
author: Saïd Zarati
reviewed by: Carles Broto
MaRDI profile type: Publication
cites work: Q3784858
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description: scientific article; zbMATH DE number 4042848