On the Higher Topological Hochschild Homology of F-p and Commutative F-p-Group Algebras Academic Article uri icon

abstract

  • We extend Torleif Veen's calculation of higher topological Hochschild homology ${sf THH}^{[n]}_*(mathbb{F}_p)$ from $nleq 2p$ to $nleq 2p+2$ for $p$ odd, and from $n=2$ to $nleq 3$ for $p=2$. We calculate higher Hochschild homology ${sf HH}_*^{[n]}(k[x])$ over $k$ for any integral domain $k$, and ${sf HH}_*^{[n]}(mathbb{F}_p[x]/x^{p^ell})$ for all $n>0$. We use this and 'etale descent to calculate ${sf HH}_*^{[n]}(mathbb{F}_p[G])$ for all $n>0$ for any cyclic group $G$, and therefore also for any finitely generated abelian group $G$. We show a splitting result for higher ${sf THH}$ of commutative $mathbb{F}_p$-group algebras and use this technique to calculate higher topological Hochschild homology of such group algebras for as large an $n$ as ${sf THH}^{[n]}_*(mathbb{F}_p) $ is known for.

published proceedings

  • WOMEN IN TOPOLOGY: COLLABORATIONS IN HOMOTOPY THEORY

author list (cited authors)

  • Bobkova, I., Lindenstrauss, A., Poirier, K., Richter, B., & Zakharevich, I.

citation count

  • 6

complete list of authors

  • Bobkova, Irina||Lindenstrauss, Ayelet||Poirier, Kate||Richter, Birgit||Zakharevich, Inna

publication date

  • January 2015