Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches.
Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content.
Contact customer_support@projecteuclid.org with any questions.
View Project Euclid Privacy Policy
We study the universal minimal ordinary Galois deformation of an induced representation from a real quadratic field with values in . By Taylor–Wiles, the universal ring is isomorphic to a local ring of a Hecke algebra. Combining an idea of Cho–Vatsal [CV03] with a modified Taylor–Wiles patching argument in [H17], under mild assumptions, we show that the Pontryagin dual of the adjoint Selmer group of is canonically isomorphic to for a non-zero divisor which is a generator of the different of over the weight Iwasawa algebra inside . Moreover, defining for a fundamental unit of the real quadratic field , we show that the adjoint Selmer group of for the (minimal) universal character deforming is isomorphic to as -modules.
Information
Published: 1 January 2020
First available in Project Euclid: 12 January 2021
Digital Object Identifier: 10.2969/aspm/08610351
Subjects:
Primary:
11F25
,
11F33
,
11F80
,
11R23
Secondary:
11F11
,
11F27
,
11G18
Keywords:
adjoint Selmer group
,
cyclicity
,
Galois deformation ring
,
Hecke algebra