4 problems

Product and ascending base-change conjecture. (1) The compositum of two $l$-$i$-modular extensions is $l$-$i$-modular: if $K/k$ and $L/k$ are $l$-$i$-modular, then $K(L)/k$ is $l$-…

Let $\cE$ be the symmetry category, let $\cC$ be a non-degenerate unitary braided fusion category over $\cE$, and let $\cM$ be a modular extension of $\cC$. Let $c$ be the central…

Let $G^f$ be a fermionic symmetry group and let $\cE=\operatorname{sRep}(G^f)$ be the corresponding symmetric fusion category. Let $\cM$ be a modular extension of $\cE$, and let…

Let $G$ be a symmetry group and let $\cE=\operatorname{Rep}(G)$. A modular extension $\cM$ of $\cE$ is a UMTC containing $\cE$ fully faithfully and satisfying the defining centrali…