On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields

  • Fabien Trihan

    Department of Information and Communication Sciences, Sophia University, Chiyoda-ku, Tokyo, 102-0081, Japan
  • David Vauclair

    Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Normandie, BP 5186, 14032 Caen Cedex, France
On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields cover
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Abstract

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. 473–522

DOI 10.4171/DM/686