A note on K-theory and triangulated categories

By M. Schlichting. 2002

76 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e8bd51249e6c9481223b01e35de75038f44f4c3

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On exact $\infty$-categories and the Theorem of the Heart (2012, methodology): “Amnon Nee-man has provided an analogous result for his K -theory of triangulated categories [24]; given Neeman’s result, our result here may be alternatively summarized as saying that the Waldhausen K -theory of a stable ∞ -category A with a bounded t-structure agrees with Neeman’s K -theory of the…”
Topological equivalences for differential graded algebras (2006, background): “The dgas R and S arise in connection with the stable module categories discussed in [ Sch ].”
A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “On the other hand, the fact that the two model categories are not Quillen equivalent is a deep result, whose original proof in [55] uses rather involved K-theoretical computations.”
Notes on Motives in Finite Characteristic (2007, background): “ an autoequivalence given 21It is well-known that in order to deﬁne a correct K-theory one needs either an appropriate enrichment on HomB(X,Y ), or a model structure in the sense of Quillen, see e.g. [10]. 22Enriched by abelian groups in the plain sense (without higher homotopies). 30 by the inverti”
A remark on K-theory and S-categories (2002, background): “Proof: Let M1 := mM(Z/p2) and M2 := mM(Z/p[ ]) be the two stable model categories considered in [20].”
On the algebraic K‐theory of higher categories (2012, background): “The idea is that the algebraic K-theory of a ring or scheme should by approximation depend (in some sense) only on a derived category of perfect modules; however, this form of K-theory has known limitations: an example of Marco Schlichting [62] shows that Waldhausen K-theory can distinguish stable ∞”