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

In this article, we prove (many parts of) the rank two case of the Kato'slocal epsilon-conjecture using the Colmez's p-adic local Langlandscorrespondence for GL_2(Q_p). We show that a Colmez's pairing defined in hisstudy of locally algebraic vectors gives us the conjecturalepsilon-isomorphisms for (almost) all the families of p-adic representations ofGal(overline{Q}_p/Q_p) of rank two, which satisfy the desired interpolationproperty for the de Rham and trianguline case. For the de Rham and nontrianguline case, we also show this interpolation property for the "critical"range of Hodge-Tate weights using the Emerton's theorem on the compatibility ofclassical and p-adic local Langlands correspondence. As an application, weprove that the Kato's Euler system associated to any Hecke eigen new formsatisfies a functional equation which has the same form as predicted by theKato's global epsilon-conjecture.

Local epsilon-isomorphisms for rank two p-adic representations of Gal(overline{Q}_p/Q_p) and a functional equation of Kato's Euler system