We identify the equivariant structure of filtered pieces motivic filtration defined by Bhatt, Morrow and Scholze on topological Hochschild cohomology spectrum polynomial algebras over Fp.

Let G be a finite group, F an algebraically closed field of finite characteristic p, and let B be a block of FG. We show that the Hochschild and Linckelmann cohomology rings of B are isomorphic, modulo their radicals, in the cases where (1) B is cyclic and (2) B is arbitrary and G either a nilpotent group or a Frobenius group (p odd). (The second case is a consequence of a more general result)....

Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. The Harrison component of Hochschild cohomology, vanishing on smooth manifolds, reflects information about singularities. The Harrison 2–cochains are symmetric and are interpreted in terms of abelian ∗–products. This paper begins a study of abelian quantization on plane curves over C, b...

Associated with each of the classical cohomology theories in algebra has been a theory relating H (H as classically numbered) to obstructions to non-singular extensions and H with coefficients in a “center” to the non-singular extension theory (see [Eilenberg & MacLane (1947), Hochschild (1947), Hochschild (1954), MacLane (1958), Shukla (1961), Harrison (1962)]). In this paper we carry out the ...

We compute the A 1 -localization of several invariants schemes namely, topological Hochschild homology ( THH ), cyclic TC ) and periodic TP ). This procedure is quite brutal kills completed versions most these invariants. The main ingredient for vanishing statements de Rham cohomology (and, eventually, crystalline cohomology) in positive characteristics.