The Distribution and Growth of the Elementary Divisors of the Reductions of an Elliptic Curve over a Function Field
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چکیده
Let K be a global field of characteristic p ≥ 5 and let E/K be a non-isotrivial elliptic curve. For places v of K of good reduction for E, let Ev/kv be the reduction of E modulo v. Then Ev(kv) ' Z/dvZ × Z/dvevZ for positive integers dv , ev , uniquely determined by E and v. We study the distribution of dv and the growth of dvev as v varies over places of degree n and n→∞.
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تاریخ انتشار 2012