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

We study the Eisenstein ideal for modular forms of even weight $k>2$ andprime level $N$. We pay special attention to the phenomenon of $\mathit{extra \reducibility}$: the Eisenstein ideal is strictly larger than the ideal cuttingout reducible Galois representations. We prove a modularity theorem for theseextra reducible representations. As consequences, we relate the derivative of aMazur-Tate $L$-function to the rank of the Hecke algebra, generalizing atheorem of Merel, and give a new proof of a special case of an equivariant mainconjecture of Kato. In the second half of the paper, we recall Kato'sformulation of this main conjecture in the case of a family of motives given bytwists by characters of conductor $N$ and $p$-power order and its relation toother formulations of the equivariant main conjecture.

The Eisenstein ideal for weight k and a Bloch-Kato conjecture for tame families