Growth of Selmer Groups over function fields
Aftab Pande

TL;DR
This paper investigates the growth of the p-Selmer group ranks of abelian varieties over function fields, establishing lower bounds in dihedral extensions using Mazur-Rubin's local constants theory.
Contribution
It extends the understanding of Selmer group growth to function fields, applying local constants theory to relate ranks over quadratic and dihedral extensions.
Findings
If the Z_p-corank of Sel_p(A/K) is odd, then Z_p-corank of Sel_p(A/F) is at least [F:K].
The results connect Selmer group growth with extension degrees in function fields.
Uses Mazur-Rubin local constants theory for elliptic curves over number fields, adapted to function fields.
Abstract
We study the rank of the -Selmer group of an abelian variety , where is a function field. If is a quadratic extension and is a dihedral extension and the -corank of is odd, we show that the -corank of . The result uses the theory of local constants developed by Mazur-Rubin for elliptic curves over number fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Meromorphic and Entire Functions
