On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields
Fabien TrihanDepartment of Information and Communication Sciences, Sophia University, Chiyoda-ku, Tokyo, 102-0081, Japan
David VauclairLaboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie, BP 5186, 14032 Caen Cedex, France
We establish the Iwasawa main conjecture for semistable abelian varieties over a function field of characteristic under certain restrictive assumptions. Namely we consider -torsion free -adic Lie extensions of the base field which contain the constant -extension and are everywhere unramified. Under the usual hypothesis, we give a proof which mainly relies on the interpretation of the Selmer complex in terms of -adic cohomology [F. Trihan, D. Vauclair, A comparison theorem for semi abelian schemes over a smooth curve, preprint arXiv:1505.02942, 2015] together with the trace formulas of J.-Y. Etesse and B. Le Stum [Math. Ann. 296, No. 3, 557--576 (1993; Zbl 0789.14015)].
Cite this article
Fabien Trihan, David Vauclair, On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields. Doc. Math. 24 (2019), pp. 473–522DOI 10.4171/DM/686