Reduced power operations in motivic cohomology

Convergence of the Motivic Adams Spectral Sequence

“…The structure of the dual Steenrod algebra is determined by Voevodsky [20], with a gap filled in [21] (see also [9]). One has ( [20], Theorem 12.6):…”

“…Actually, as shown in [20], (HZ/2 * , A * ) is not a Hopf algebra but a Hopf algebroid; in (8), θ is identified with η L θ. If one uses η R θ instead, one gets an additional term, which is why the formula in Theorem 12.6 of [20] looks slightly different.…”

“…If one uses η R θ instead, one gets an additional term, which is why the formula in Theorem 12.6 of [20] looks slightly different. This structure theorem will be needed in the remaining sections.…”

The Hopf condition for bilinear forms over arbitrary fields

“…When n > 1 the calculation gives H 2,1 (DQ n ; Z/2) ∼ = Z/2, and we let b denote the unique nonzero element. For n = 1 we have DQ 1 ∼ = A 1 − 0, and it is known that H 2,1 (A 1 − 0; Z/2) = 0 (see, for instance, [V1,Lem. 6.8]).…”

T-spectra and Poincaré duality

“…To embellish the latter result, let us mention that unlike the topological context in algebro-geometrical case the canonical pairing H * , * M (X)⊗H M * , * (X) → H * , * M (pt) is generally degenerated even with rational coefficients [Vo2].…”