### A quantitative Fontaine-Mazur analogue for function fields, by Joshua Holden

Let k be a function field over a finite field F of characteristic p and
order q, and l a prime not equal to p. Let K = k
F_{l∞} be obtained from k by taking the maximal
l-extension of the constant field. If M is an unramified l-adic analytic
l-extension of k, and M does not contain K, must M be a finite extension of
k? The answer is, in general, ``no'', but for some k the answer is
``yes''. We attempt to estimate the proportion of k with each answer.

Joshua Holden <holden@math.duke.edu>