Is there a common general setup for both Weil cohomologies and generalized cohomology theories?

2011-04-13T22:58:06Z

My question can be simply (and loosely) stated as follows:

Is there a general (but not too general) construction that captures, as specializations, both Weil cohomologies in algebraic geometry and generalized cohomology theories in topology ?

(I must say I'm not an expert of any of the two!)

Answer by SGP for Is there a common general setup for both Weil cohomologies and generalized cohomology theories?

2011-04-13T23:14:28Z

It would appear that the answer to the question as stated is no. However, Voevodsky's motivic homotopy theory does provide an adequate framework for both Weil cohomologies and generalized cohomology theories; there is a version of "Brown representability" theorem (representing object for a generalized cohomology theory) which is exploited in the applications to K-theory (Milnor conjecture and Bloch-Kato conjecture).

Is there a common general setup for both Weil cohomologies and generalized cohomology theories? - MathOverflow

Is there a common general setup for both Weil cohomologies and generalized cohomology theories?

Answer by SGP for Is there a common general setup for both Weil cohomologies and generalized cohomology theories?