301 research outputs found
Isogeny and overconvergence
No full textIn this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field K of characteristic p are isogenous. Specifically, assuming that their endomorphism algebras tensored with Qp are division algebras, we prove that if the maximal quotients of minimal slope (i.e., the unique maximal isoclinic quotient corresponding to the minimal slope, defined up to isogeny) of their associated p-divisible groups are isogenous, then the abelian varieties themselves are isogenous over K . We also extend this result to certain p-divisible groups, highlighting the deep connection between isogenies of abelian varieties and the structure of overconvergent F-isocrystals
A note on semistable Barsotti-Tate groups
No full textWe show that the Dieudonn\\u27e crystal associated to a Barsotti-Tate group with potentially semistable reduction over a smooth curve is overconvergent. As a corollary, we obtain the rationality of the -function associated to this group
On the non commutative Iwasawa Main Conjecture for abelian varieties over function fields
No full textInternational 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]
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