English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Kolyvagin used Heegner points to associate a system of cohomology classes toan elliptic curve over $\Q$ and conjectured that the system contains anon-trivial class. His conjecture has profound implications on the structure ofSelmer groups. We provide new computational and theoretical evidence forKolyvagin's conjecture. More precisely, we explicitly compute Heegner pointsover ring class fields and use these points to verify the conjecture forspecific elliptic curves of rank two. We explain how Kolyvagin's conjectureimplies that if the analytic rank of an elliptic curve is at least two then the$\Z_p$-corank of the corresponding Selmer group is at least two as well. Wealso use explicitly computed Heegner points to produce non-trivial classes inthe Shafarevich-Tate group.

Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group