On the abelianization of derived categories and a negative solution to Rosicky's problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10174099" target="_blank" >RIV/00216208:11320/13:10174099 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1112/S0010437X12000413" target="_blank" >http://dx.doi.org/10.1112/S0010437X12000413</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/S0010437X12000413" target="_blank" >10.1112/S0010437X12000413</a>

Result language
angličtina
Original language name
On the abelianization of derived categories and a negative solution to Rosicky's problem
Original language description
We prove for a large family of rings R that their lambda-pure global dimension is greater than one for each in finite regular cardinal lambda. This answers in the negative a problem posed by Rosicky. The derived categories of such rings then do not satisfy, for any lambda, the Adams lambda-representability for morphisms. Equivalently, they are examples of well-generated triangulated categories whose lambda-abelianization in the sense of Neeman is not a full functor for any lambda. In particular, we showthat given a compactly generated triangulated category, one may not be able to find a Rosicky functor among the lambda-abelianization functors.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GPP201%2F10%2FP084" target="_blank" >GPP201/10/P084: Modern homological algebra and geometry in representation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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