All Questions

In Discrete groups, expanding graphs, and invariant measures (in the notes at the end of Chapter 7), Lubotzky mentions that certain estimates for the number of spanning trees $\kappa(G)$ of a $k$-...

Let $X$ be a projective algebraic curve over some number field $K$, and let $\varphi:X\hookrightarrow \mathbb{P}^n_K$ be an embedding of it (defined over $K$) into some projective space. Now let $X'$ ...

My previous question about the theorem (apparently due to Dedekind -- thanks, Arturo Magidin!) that the ring $\overline{\mathbb{Z}}$ of all algebraic integers is a Bezout domain got me thinking about ...

Let $X$ be a geometrically integral smooth projective variety over a number field $k$. Then if $X$ is everywhere locally soluble, we have $Pic(X) = H^0(k,Pic (\overline{X}))$, where $\overline{X}=X \...

Let us say that an abstract number ring is an integral domain $R$ which is not a field, and which has the "finite norms" property: for any nonzero ideal $I$ of $R$, the quotient $R/I$ is finite. (I ...