Strong local-global phenomena for Galois and automorphic representations
arXiv:1511.00586
Abstract
Many results are known regarding how much local information is required to determine a global object, such as a modular form, or a Galois or automorphic representation. We survey some things that are known and expected, and then explain recent joint work with Dinakar Ramakrishnan about comparing degree 2 Artin and automorphic representations which a priori may not correspond at certain infinite sets of places.
These are notes based on a talk I gave at the RIMS workshop, "Modular forms and automorphic representations," in February 2015; 14 pages