Expanding Graphs and Arithmetic Geometry

Aquest artícle es pot trobar aquí.

Theorem.

Let K be a number field. Lete Wk be a smoth geometric connected algebraic curve defined over k. Let (Ui)i\in I be an infinite family of étale covers definde over k. Let s be a fixed set of generators of $\pi_1(U_\CC,x_0) for some x0 \in U_\CC and consider the family of graphs $C(\pi(U_\CC,x0),\pi(U_i,x_i),S) x1 over x2 Cailer-Schrein graphs, If this familiy is "Esperantist$ then the set is finite for all but finitley \bigcup_{[k:k'] = d} U_i(k'), many $i\in I$.

---------------

Aqui ve a dir que pasen coses al valor propi 1/4.