What question did this study set out to answer?

This research aims to prove Kolyvagin's conjecture regarding the non-vanishing of Kolyvagin systems derived from Heegner points for elliptic curves.

Non-vanishing of Kolyvagin systems and Iwasawa theory

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Randomized trial demonstrates non-trivial Kolyvagin systems for elliptic curves, indicating key advancements in Iwasawa theory.

This research aims to prove Kolyvagin's conjecture regarding the non-vanishing of Kolyvagin systems derived from Heegner points for elliptic curves.
Investigated Kolyvagin's conjecture for primes of good ordinary reduction that split in imaginary quadratic fields.
Used cohomology analysis of the p-adic Tate module and Heegner points to validate the conjecture.
Refined the conjecture relating Heegner point Kolyvagin systems to Tamagawa numbers.
Proved that Kolyvagin's conjecture holds for primes that split in the relevant quadratic field.
Validated a refinement relating the divisibility index of the Kolyvagin system to Tamagawa numbers of the elliptic curve.
Established analogous results for Kolyvagin systems derived from Kato's Euler system.

Burungale et al. (2026) studied this question.

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