Abstract
We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.
We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie–Weiss spectral sequences approximating the homology and homotopy of knot spaces vanish at a prime
$p$
. Combined with recent results on the relationship between embedding calculus and finite-type theory, we deduce that the
$(n+1)$
th Goodwillie–Weiss approximation is a
$p$
-local universal Vassiliev invariant of degree
$\leq n$
for every
$n \leq p + 1$
.
AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term
Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p
