Let $(X,\mathcal{O}_X)$ be a locally ringed space such that $\mathcal{O}_X$ is locally notherian, and let $\operatorname{Coh}(\mathcal{O}_X)$ be the category of coherent $\mathcal{O}_X$-modules. The inclusion $\operatorname{Coh}(\mathcal{O}_X)\rightarrow \operatorname{Mod}(\mathcal{O}_X)$ induces...

We reference [EGNO] for the concept of a braided fusion category. Following the conventions in [JFR], let $\mathcal{C}$ denote a braided fusion category equipped with a braiding $\beta$, and let $\mathcal{B} \subset \mathcal{C}$ represent a fully faithful inclusion of braided fusion categories. T...

Let $F$ be a global number field, i.e. a finite extension of the field of rational numbers. Let $\sigma$, $\pi$ be automorphic representations of $\mathrm{GL}_n(F)$ and $\mathrm{GL}_{n+1}(F)$ respectively. Let $v$ be a finite place of $F$. We consider the local $L$-factor (defined by Jacquet-Piat...

A perfect squaring of a rectangle may be defined as a partition of the rectangle into finitely many squares all of which are mutually non-congruent. https://en.wikipedia.org/wiki/Squaring_the_square shows, among other things, perfect squarings of the square with provably least number of smaller s...

Suppose $X$ is a complex abelian variety of dimension 2. Then I believe the ring of endomorphisms $\mathrm{End}(X)$, tensored with $\mathbb{C}$, is isomorphic to a subalgebra $M_2(\mathbb{C})$ of $2 \times 2$ complex matrices. This let us choose an inclusion $\mathrm{End}(X) \subset M_2(\mathbb{C...