Vol. 296, No. 2, 2018

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The action of the Hecke operators on the component groups of modular Jacobian varieties

Taekyung Kim and Hwajong Yoo

Vol. 296 (2018), No. 2, 341–355

For a prime number q 5 and a positive integer N prime to q, Ribet proved the action of the Hecke algebra on the component group of the Jacobian variety of the modular curve of level Nq at q is “Eisenstein”, which means the Hecke operator T acts by + 1 when is a prime number not dividing the level. We completely compute the action of the Hecke algebra on this component group by a careful study of supersingular points with extra automorphisms.

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Hecke operators, Hecke action, component group, modular Jacobian varieties
Mathematical Subject Classification 2010
Primary: 11G05, 11G18, 14G35
Received: 23 October 2017
Revised: 5 February 2018
Accepted: 6 February 2018
Published: 16 July 2018
Taekyung Kim
Center for Geometry and Physics
Institute for Basic Science
South Korea
Hwajong Yoo
Center for Geometry and Physics
Institute for Basic Science
South Korea