We formulate the “real integral Hodge conjecture”, a version of the integral Hodge
conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on …

Let G be an algebraic group over a field F, V a generically free representation of G (ie, the
stabilizer of the generic point in V is trivial) and U⊂ V a G-equivariant open subset such that …

Let G be an algebraic group over a field F. As defined by Serre, a cohomological invariant of
G of degree n with values in ℚ∕ ℤ (j) is a functorial-in-K collection of maps of sets Tors G …

Let A be local ring in which 2 is invertible and let n be a non-negative integer. We show that
the nth cohomological invariant of quadratic forms is a well-defined homomorphism from the …

Let G be an algebraic group over F and pa prime integer. We introduce the notion of ap-
retract rational variety and prove that if Y→ X is ap-versal G-torsor, then BG is a stable p …

In this paper, we introduce a condition (F _m'F m′) on a field K, for a positive integer m, that
generalizes Serre's condition (F) and which still implies the finiteness of the Galois …

We show a conditional exactness statement for the Nisnevich Gersten complex associated
to an A 1-invariant cohomology theory with Nisnevich descent for smooth schemes over a …

We establish an Atiyah-Hirzebruch type spectral sequence relating real morphic
cohomology and real semi-topological $ K $-theory and prove it to be compatible with the …

In various triangulated motivic categories, a vast family of aisles (these are certain classes of
objects) is introduced. These aisles are defined in terms of the corresponding “motives”(or …

Morel's stable connectivity theorem states the vanishing of the sheaves of the negative
motivic homotopy groups π¯ is⁢(Y) and π¯ i+ j, js⁢(Y), i< 0, in the stable motivic homotopy …