Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem
نویسندگان
چکیده
منابع مشابه
K-theory and Derived Equivalences
We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.
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Deenition: A derived category ... is when you take complexes seriously! (L.L. Scott Sc]) The aim of this chapter is to give a fairly elementary introduction to the (not very elementary) subject of derived categories and equivalences. Especially, we emphasize the applications of derived equivalences in representation theory of groups and algebras in order to illustrate the importance and usefuln...
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The main purpose of the present article is to establish the real case of “Karoubi’s Conjecture” [20] in algebraic K-theory. The complex case was proved in 1990-91 (cf. [32] for the C∗-algebraic form of the conjecture, and [38] for both the Banach and C∗-algebraic forms). Compared to the case of complex algebras, the real case poses additional difficulties. This is due to the fact that topologic...
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One purpose of this paper is to improve the periodicity theorem of Hermitian K-theory proved in [6 ], using some recent results by A..J. Berrick and the author [1]. For instance, if 1/2 [ A we show that the “higher Witt groups” εWn(A), defined for a ring A with antiinvolution (ε being the sign of symmetry), are periodic of period α ≠ 0 mod. 4, with a control of the 2-torsion depending on α. Mor...
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Rognes andWeibel used Voevodsky’s work on the Milnor conjecture to deduce the strong Dwyer-Friedlander form of the Lichtenbaum-Quillen conjecture at the prime 2. In consequence (the 2-completion of) the classifying space for algebraic K-theory of the integers Z[1/2] can be expressed as a fiber product of wellunderstood spaces BO and BGL(F3) over BU . Similar results are now obtained for Hermiti...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2017
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2016.12.026