Hecke operators, the Eichler-Shimura relation and an introduction to modularity
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| Full text | |
| Author(s): |
Alvarenga, Roberto
Total Authors: 1
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| Document type: | Journal article |
| Source: | JOURNAL OF NUMBER THEORY; v. 199, p. 192-228, JUN 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms. Let X be a curve over F-q, F its function field and A the adele ring of F. In this paper we will exhibit the first properties for the graph of Hecke operators for GL(n)(A), for every n >= 1. This includes a description of the graph in terms of coherent sheaves on X. We provide a numerical condition for two vertices to be connected by an edge. Moreover, we describe how to calculate these graphs in the case of the projective line X = P-1(F-q). (C) 2018 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 17/21259-3 - Graphs of Hecke Operators and Rational Points |
| Grantee: | Roberto Carlos Alvarenga da Silva Junior |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |