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We discuss various connections between ideal classes, divisors, Picard and Chow groups of one-dimensional noetherian domains. As a result of these, we give a method to compute Chow groups of orders in global fields and show that there are infinitely many number fields which contain orders with trivial Chow groups. [ABSTRACT FROM AUTHOR]

We show how our p-adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is the use of "moduli-friendly" Eisenstein series introduced by Makdisi, which allow us to evaluate modular forms at p-adic points of modular curves and dispenses us of the need for equations of modular curves and for q-expansion computations in the construction of models of modular Jacobians. The resulting algorithm compares very favourably to our complex-analytic method. [ABSTRACT FROM AUTHOR]

Let K be a complete, algebraically closed non-Archimedean valued field, and let $$\varphi (z) \in K(z)$$ have degree two. We describe the crucial set of $$\varphi $$ in terms of the multipliers of $$\varphi $$ at the classical fixed points, and use this to show that the crucial set determines a stratification of the moduli space $$\mathcal {M}_2(K)$$ related to the reduction type of $$\varphi $$ . We apply this to settle a special case of a conjecture of Hsia regarding the density of repelling periodic points in the classical non-Archimedean Julia set. [ABSTRACT FROM AUTHOR]