Geodesic
On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields
Documenta mathematica, Tome 24 (2019), pp. 473-522
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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 Zp​-extension and are everywhere unramified. 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 [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)].
DOI : 10.4171/dm/686
Classification : 11G05, 11G10, 11R23, 11R34, 11R42, 11R58, 11S40
Mots-clés : Iwasawa theory, abelian variety, p-adic cohomology, syntomic, non-commutative 
@article{10_4171_dm_686,
     author = {David Vauclair and Fabien Trihan},
     title = {On the {Non} {Commutative} {Iwasawa} {Main} {Conjecture} for {Abelian} {Varieties} over {Function} {Fields}},
     journal = {Documenta mathematica},
     pages = {473--522},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/686},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/686/}
}
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David Vauclair; Fabien Trihan. On the Non Commutative Iwasawa Main Conjecture for Abelian Varieties over Function Fields. Documenta mathematica, Tome 24 (2019), pp. 473-522. doi: 10.4171/dm/686

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