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math.NT2026
Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields
Jordan S. Ellenberg, Aaron Landesman
We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer groups of quadratic twist families of abelian varieties over global function fields. As a consequ…
math.NT2025
Smyth's conjecture and a non-deterministic Hasse principle
Jordan S. Ellenberg, Will Hardt
In a 1986 paper, Smyth proposed a conjecture about which integer-linear relations were possible among Galois-conjugate algebraic numbers. We prove this conjecture. The main tools (…