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The n ‐order of algebraic triangulated categories
Author(s) -
Schwede Stefan
Publication year - 2013
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtt014
Subject(s) - mathematics , algebraic number , homotopy , order (exchange) , homotopy category , pure mathematics , triangulated category , prime (order theory) , invariant (physics) , combinatorics , algebra over a field , discrete mathematics , derived category , mathematical analysis , functor , finance , economics , mathematical physics
We quantify certain features of algebraic triangulated categories using the ‘ n ‐order’, an invariant that measures how strongly n annihilates objects of the form Y / n . We show that the n ‐order of an algebraic triangulated category is infinite, and that the p ‐order of the p ‐local stable homotopy category is exactly p −1 for any prime p . In particular, the p ‐local stable homotopy category is not algebraic.