On the integral Hodge conjecture for real varieties, II

Theorem A. Let X be a smooth projective variety defined over an alge- braically closed non-Archimedean complete field k of residue characteristic zero.. on every compact subset of

— We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if W is such a variety,

The following corollary follows immediately from the fact that an arbitrary algebraic extension field of Q is the direct limit of certain algebraic number fields and from the fact

The purpose of this paper is to show the validity of the Generalized Hodge Conjecture for stably nondegenerate abelian varieties all of whose simple components are of

Tadic, Unitary representations of the general linear group over the real and complex fields, preprint. [V]

Here, the construction of L A/K ∞ , the proof that N K ∞ is torsion and the proof of (3) are simultaneous and rely essentially on the main result of [TV] (a sheaed version of [KT]

The above exact sequence then gives the prime-to-p part of the main theorem of unramified class field theory for surfaces over a finite field (studied by Parshin, Bloch,

Our proof combines geometric ideas in her paper with tools from algebraic K -theory (motivic homology, unramified cohomology)... Unramified cohomology of degree 3 and integral