ON THE NON COMMUTATIVE IWASAWA MAIN CONJECTURE FOR ABELIAN VARIETIES OVER FUNCTION FIELDS

We establish the Iwasawa main conjecture for semistable abelian varieties over a function field of characteristic p under certain restrictive assumptions. Namely we consider p-torsion free p-adic Lie extensions of the base field which contain the constant Z(p)-extension and are everywhere unramified. Under the usual mu = 0 hypothesis, we give a proof which mainly relies on the interpretation of the Selmer complex in terms of p-adic cohomology [TV] together with the trace formulas of [EL1].