MathOverflow

Setup
Let $E/K$ be a ramified quadratic extension of local fields of residue characteristic$2$, with nontrivial automorphism $z \mapsto z^*$, valuation ring $\mathcal{O}$, andnormalized valuation $v$; ramification gives $v(z^*) = v(z)$ and$v(K^\times) = 2...

For finite simple graphs, there is a substantial literature on those determined by their adjacency spectrum (DS). In particular, I understand that a widely held conjecture (and several partial results) suggest that almost all finite graphs are determined...

Which number fields are generated by the units of some number field? That is, if $K$ is a number field and $U(K)$ its group of units, the field $k = \mathbb{Q}(U(K))$ is a subfield of $K$. But which number fields $k$ occur in this way as $K$ varies over...

For a generic non-CM abelian variety $A/\mathbb{Q}$ of dimension $>1$, is it conjectured that the set of supersingular primes of $A$ is (in)finite?
I know that this set is known to have density $0$ by this paper, but I am wondering whether one expects an analogue of Elkies' theorem for elliptic curves, namely finiteness rather than merely density $0$. In some cases, infiniteness of supersingular...