On the non commutative Iwasawa Main Conjecture for abelian varieties over function fields

International audienceWe establish the Iwasawa main conjecture for semistable abelian varieties over a function eld of characteristic p under certain restrictive assumptions. Namely we consider p-torsion free p-adic Lie extensions of the base eld which contain the constant Z p-extension and are everywhere unramied. Under the usual µ = 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]