Addendum to "Čech and Steenrod homotopy theory with applications to geometric topology"
Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.
For a prime , we compute the algebraic -theory modulo and of the mod Adams summand, using topological cyclic homology. On the way, we evaluate its modulo and topological Hochschild homology. Using a localization sequence, we also compute the -theory modulo and of the first Morava -theory.
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
In this paper we present an approximation to the de Rham theorem for simplicial sets with any coefficients based, using simplicial techniques, on Poincaré's lemma and q-extendability.