MathOverflow

When I say that $x$ is a Dedekind real, I mean that $x$ is a left Dedekind cut of the rational numbers; that is, $x \subseteq \mathbb{Q}$ satisfying the following properties:
$\exists r,s \in \mathbb{Q} (r \in x \wedge s \notin x)$.
If $q \in x$ and $r \in \mathbb{Q}$ with $r < q$, then $r \in x$....

Let $C$ be a smooth projective geometrically connected curve of genus 2 defined over a number field $k$. Here are some definitions:
The index $I$ of a curve $C$ is the greatest common divisor of all effective divisors $D \in \mathrm{Div}(C)$. Equivalently, it is the greatest common divisor of the degrees $[L:k]$, where $[L:k]$ ranges over algebraic extensions such that $C(L) \neq...

Dedekind gave an example of a number field whose ring of integers does not have a power integral basis, namely $\mathbb{Q}(r)$, where $r^3-r^2-2r-8=0$. The discriminant of this field is $\Delta=-503$. Note that $\Delta \equiv 1 \pmod 4$. If the discriminant...

Let $m\geq 3$, and let$$\rho:\overline{M}_{0,m+1,\mathbb{C}}\to \overline{M}_{0,m,\mathbb{C}}$$be the universal curve. Fix$$s_0=[B_0,p_1,\ldots,p_m]\in \overline{M}_{0,m,\mathbb{C}}(\mathbb{C})$$and identify the fiber $\rho^{-1}(s_0)$ with $B_0$. Let...