Rational isomorphisms between K-theories and cohomology theories

Rational Isomorphisms between K-theories and Cohomology Theories

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the “Segre map”) of infinite loop spaces. Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced which establishe...

Cohomology Theories

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Eqüivariant Cohomology Theories

Throughout this note G denotes a discrete group. A G-complex is a CPP-complex on which G acts by cellular maps such that the fixed point set of any element of G is a subcomplex. On the category of pairs of G-complexes and equivariant homotopy classes of maps, an equivariant cohomology theory is a sequence of contravariant functors 3C into the category of abelian groups together with natural tra...

Cohomology of Algebraic Theories

Generalised sheaf cohomology theories

This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled “Homotopy Theory of Geometric Categories” on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002. The intent for the lec...