5 problems

Let $p\in\mathbb N$ be prime, let $K=\mathbb Q[\sqrt{p}]$, and let $R_p$ be the order of index $p$ in $K$. An order is locally associated when it has the local association property…

Graduated-order conjecture. The order $H_{n,\lambda}$, represented as a matrix order using the standard basis of $S_\lambda(V)$, is a graduated order: there exists a matrix…

Lattice-power invertibility conjecture. The lattice $\mathfrak c^{n-1}$ and every higher power $\mathfrak c^m$ with $m\geq n-1$ are invertible in their common endomorphism ring.

Let $C$ be the canonically embedded complete-intersection curve of degree $8$ and genus $5$ arising as the base locus of a net of quadrics in $\mathbb{P}^4$. Fix ramification data…

Let $Q$ be a conic bundle and let $\operatorname{Cl}_0(Q)$ be its even Clifford algebra. Consider orders Morita equivalent to $\operatorname{Cl}_0(Q)$ and having the same rank and…