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

Let $p>3$ be a prime. In this paper we develop a new kind of anticyclotomiclocal $\pm$-Iwasawa theory at $p$ for Hecke characters of quadratic imaginaryfields which is valid for all ramification types of $p$ (split, inert andramified). As an application we deduce the converse of Gross-Zagier-Kolyvagintheorem for these CM forms, which states that Selmer rank one implies analyticrank one. To carry out the Iwasawa theory argument we employ a recentconstruction of a new type of $p$-adic $L$-function by Andreatta-Iovita, andgeneralized by Yangyu Fan to Shimura curves in the Appendix, and a ``virtualHeenger family'' made via a limiting procedure from a Heegner family alongColeman-Mazur eigencurve constructed by Jetchev-Loeffler-Zerbes.

A New $\pm$ Iwasawa Theory and Converse of Gross-Zagier and Kolyvagin Theorem (with an Appendix by Yangyu Fan)