6 problems

For an integer $n\geqslant2$, let $\mathbb{Z}_{\!/2}^n$ denote the direct sum of $n$ copies of the cyclic group $\mathbb{Z}_{\!/2}$. Let $\lambda(\mathbb{Z}_{\!/2}^n)$ denote its L…

Conjectural tensor-product formulae.

Let $r\in\mathbb{Z}_{>1}$, let $G=C_p^r$, and let $X=St_{r-1}$ via an embedding $C_p^r<\Bbbk^+<SL_2(\Bbbk)$. For a faithful $G$-module $X$, let $\mathcal{T}_X$ be the full subcateg…

Let $\Bbbk$ be an algebraically closed field of characteristic $p>0$, let $E\simeq C_p^r$ be an elementary abelian $p$-group, and fix an embedding $E<\Bbbk^+<SL_2(\Bbbk)$. Let…

For an odd prime $p$, an elementary abelian $p$-group is a group isomorphic to $(\mathbb{Z}/p\mathbb{Z})^r$. Nonexistence conjecture for elementary abelian class groups. No element…

Let $C$ be an elementary abelian $p$-group of rank $c$, and let $\rho$ be a faithful $n$-dimensional complex representation of $C$. Let $e(\rho)$ be the top degree of the indecompo…