Cohomological quotients and smashing localizations
Krause H (2005)
American Journal of Mathematics 127(6): 1191-1246.
Zeitschriftenaufsatz
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Einrichtung
Abstract / Bemerkung
The quotient of a triangulated category modulo a subcategory was defined by Verdier.
Motivated by the failure of the telescope conjecture, we introduce a new type of quotients for any
triangulated category which generalizes Verdier’s construction. Slightly simplifying this concept,
the cohomological quotients are flat epimorphisms, whereas the Verdier quotients are Ore localiza-
tions. For any compactly generated triangulated category S, a bijective correspondence between the
smashing localizations of S and the cohomological quotients of the category of compact objects in
S is established. We discuss some applications of this theory, for instance the problem of lifting
chain complexes along a ring homomorphism. This is motivated by some consequences in algebraic
K-theory and demonstrates the relevance of the telescope conjecture for derived categories. Another
application leads to a derived analogue of an almost module category in the sense of Gabber-Ramero.
It is shown that the derived category of an almost ring is of this form
Erscheinungsjahr
2005
Zeitschriftentitel
American Journal of Mathematics
Band
127
Ausgabe
6
Seite(n)
1191-1246
eISSN
1080-6377
Page URI
https://pub.uni-bielefeld.de/record/2980484
Zitieren
Krause H. Cohomological quotients and smashing localizations. American Journal of Mathematics. 2005;127(6):1191-1246.
Krause, H. (2005). Cohomological quotients and smashing localizations. American Journal of Mathematics, 127(6), 1191-1246. https://doi.org/10.1353/ajm.2005.0041
Krause, Henning. 2005. “Cohomological quotients and smashing localizations”. American Journal of Mathematics 127 (6): 1191-1246.
Krause, H. (2005). Cohomological quotients and smashing localizations. American Journal of Mathematics 127, 1191-1246.
Krause, H., 2005. Cohomological quotients and smashing localizations. American Journal of Mathematics, 127(6), p 1191-1246.
H. Krause, “Cohomological quotients and smashing localizations”, American Journal of Mathematics, vol. 127, 2005, pp. 1191-1246.
Krause, H.: Cohomological quotients and smashing localizations. American Journal of Mathematics. 127, 1191-1246 (2005).
Krause, Henning. “Cohomological quotients and smashing localizations”. American Journal of Mathematics 127.6 (2005): 1191-1246.