An explicit cycle map for the motivic cohomology of real varieties

作者：dos Santos Pedro F^*; Hardt Robert M; Lewis James D; Lima Filho Paulo

来源：Commentarii Mathematici Helvetici, 2017, 92(3): 429-465.

DOI：10.4171/CMH/416

• Ordinary equivariant cohomology
• motivic cohomology
• cycle map
• finite analytic currents
• real varieties

We provide a direct construction of a cycle map in the level of representing complexes from the motivic cohomology of real (or complex) varieties to the appropriate ordinary cohomology theory. For complex varieties, this is simply integral Betti cohomology, whereas for real varieties the recipient theory is the bigraded Gal(C/R)-equivariant cohomology [19]. Using the finite analytic correspondences from [7] we provide a sheaf-theoretic approach to ordinary equivariant RO(G)-graded cohomology for any finite group G. In particular, this gives a complex of sheaves Z(p)omega on a suitable equivariant site of real analytic manifolds-withcorner whose construction closely parallels that of the Voevodsky's motivic complexes Z(p)M.

• 出版日期2017