# Papers and preprints

- Jordan S. Ellenberg and Daniel Rayor Hast, Rational points on solvable curves over Q via non-abelian Chabauty (submitted).
We study the Selmer varieties of smooth projective curves of genus at least two defined over Q which geometrically dominate a curve with CM Jacobian. We extend a result of Coates and Kim to show that Kim's non-abelian Chabauty method applies to such a curve. By combining this with results of Bogomolov–Tschinkel and Poonen on unramified correspondences, we deduce that any cover of P

^{1}with solvable Galois group, and in particular any superelliptic curve over Q, has only finitely many rational points over Q. - Daniel Hast and Vlad Matei, Higher moments of arithmetic functions in short intervals: a geometric perspective (submitted).
We study the geometry associated to the distribution of certain arithmetic functions, including the von Mangoldt function and the Möbius function, in short intervals of polynomials over a finite field F

_{q}. Using the Grothendieck-Lefschetz trace formula, we reinterpret each moment of these distributions as a point-counting problem on a highly singular complete intersection variety. We compute part of the l-adic cohomology of these varieties, corresponding to an asymptotic bound on each moment for fixed degree n in the limit as q → ∞. The results of this paper can be viewed as a geometric explanation for asymptotic results that can be proved using analytic number theory over function fields.