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 paper, we consider Galois representations of the absolute Galoisgroup $\text{Gal}(\overline {\mathbb Q}/\mathbb Q)$ attached to modular formsfor noncongruence subgroups of $\text{SL}_2(\mathbb Z)$. When the underlyingmodular curves have a model over $\mathbb Q$, these representations areconstructed by Scholl and are referred to as Scholl representations, which forma large class of motivic Galois representations. In particular, by a result ofBelyi, Scholl representations include the Galois actions on the Jacobianvarieties of algebraic curves defined over $\mathbb Q$. As Schollrepresentations are motivic, they are expected to correspond to automorphicrepresentations according to the Langlands philosophy. Using recentdevelopments in the automorphy lifting theorem, we obtain various automphy andpotential automorphy results for potentially $\text{GL}_2$-type Galoisrepresentations associated to noncongruence modular forms. Our results areapplied to various kinds of examples. Especially, we obtain potentialautomorphy results for Galois representations attached to an infinite family ofspaces of weight 3 noncongruence cusp forms of arbitrarily large dimensions.

Potentially $\text{GL}_2$-type Galois representations associated to noncongruence modular forms