On the Mordell-Weil Ranks of supersingular abelian varieties over\n \ℤ_p²-extensions

2021/12/01 by Cédric Dion, Dion, Cédric, Jishnu Ray +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2112.00280

Abstract

Let p be a fixed odd prime and let K be an imaginary quadratic field in\nwhich p splits. Let A be an abelian variety defined over K with\nsupersingular reduction at both primes above p in K. Under certain\nassumptions, we give a growth estimate for the Mordell--Weil rank of A over\nfinite extensions inside the \ℤ_p²-extension of K. In the last\nsection, written by Chris Williams, he includes some speculative remarks on the\np-adic L-functions for \GSp(4) corresponding to the multi-signed\nSelmer groups constructed in this paper.\n

Citations

• Limites de représentations cristallines

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