The Shafarevich-Tate group in cyclotomic Z_p-extensions at supersingular primes
Florian Sprung
TL;DR
This paper investigates the growth of the p-primary Shafarevich-Tate group in cyclotomic Z_p-extensions at supersingular primes, extending previous work and linking it to Iwasawa invariants of modified Selmer groups.
Contribution
It generalizes existing results on the asymptotic behavior of the Shafarevich-Tate group at supersingular primes using Iwasawa theory.
Findings
Derived formulas for the growth of the Shafarevich-Tate group
Connected Iwasawa invariants to the behavior of Selmer groups
Extended previous results to all odd primes with supersingular reduction
Abstract
We study the asymptotic growth of the p-primary component of the Shafarevich-Tate group in the cyclotomic direction at any odd prime of good supersingular reduction, generalizing work of Kobayashi. This explains formulas obtained by Kurihara, Perrin-Riou, and Nasybullin in terms of Iwasawa invariants of modified Selmer groups.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Finite Group Theory Research