Geodesic
On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields
Documenta mathematica, Tome 24 (2019), pp. 473-522.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $\mathbb{Z}_p$-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 [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 \textit{J.-Y. Etesse} and \textit{B. Le Stum} [Math. Ann. 296, No. 3, 557--576 (1993; Zbl 0789.14015)].
Classification : 11S40, 11R23, 11R34, 11R42, 11R58, 11G05, 11G10
Keywords: abelian variety, Iwasawa theory, \(p\)-adic cohomology, syntomic, non-commutative 
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     author = {Trihan, Fabien and Vauclair, David},
     title = {On the {Non} {Commutative} {Iwasawa} {Main} {Conjecture} for {Abelian} {Varieties} over {Function} {Fields}},
     journal = {Documenta mathematica},
     pages = {473--522},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a49/}
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Trihan, Fabien; Vauclair, David. On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields. Documenta mathematica, Tome 24 (2019), pp. 473-522. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a49/