9 problems

Let $G$ be a compact $p$-adic analytic group. Write $\Omega_G$ for its completed group algebra over the coefficient ring used in the paper. Call $G$ dihedral-free if every orbital…

Chor–Lemke–Mador conjecture. There exists a positive constant $C$ such that

Let $\mathbb{C}_n$ be the Clifford algebra with generators $i_1,\ldots,i_{n-1}$, and let $\mathbb{Z}[i_1,\ldots,i_{n-1}]$ be the indicated Clifford order. A maximal order is closed…

Let $\mathcal{O}_{5,!}$ be the oddball maximal order, and let $\operatorname{Vec}(\mathcal{O}_{5,!})$ denote its vector part. A right ideal generated by…

Let $C\subset \mathbb{F}_2^n$ be a maximal doubly even binary code, and let $I=(i_0,i_1,\ldots,i_{n-1})$. Consider the Clifford algebra $\mathbb{C}_n$ and the rational Clifford alg…

Let $T$ be the algebra in the paper's main theorems, let $Q_{\operatorname{gr}}(T)$ denote its graded quotient ring, and consider graded overrings…

Let $A$ be a quaternion algebra over the field $K$ considered in the paper, and let a maximal order in $A$ have a norm-one group, meaning the subgroup of elements of reduced norm o…

Let $R$ be the ring of algebraic integers in a number field $K$, and let $A$ be an $R$-algebra that is finitely generated and projective as an $R$-module. For each maximal ideal…

Let $E$ be the elliptic curve and let $T(\mathbf{d})$ be the algebra associated to an effective divisor $\mathbf{d}$ on $E$ as in Theorem 9. Let $M$ be a finitely generated $g$-div…