Work

Class groups and local indecomposability for non-CM forms

Year: 2021

Type: article

Abstract: In the late 1990s, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those p -ordinary cuspidal eigenforms whose associated Galois representation becomes decomposable upon restriction to a decomposition group at p . It is expected that such p -ordinary eigenforms are precisely those with complex multiplication. In this paper, we study Coleman–Greenberg’s question using Galois deformation theory. In particular, for p -ordinary eigenforms which are congruent to one with complex multiplication, we prove that the conjectured answer follows from the p -indivisibility of a certain class group.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1107

Authors: Francesc Castella, Carl Wang-Erickson, Haruzo Hida

Institutions: University of California, Santa Barbara, University of Pittsburgh, University of California, Los Angeles

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, European Commission, Engineering and Physical Sciences Research Council, H2020 European Research Council