Integral period relations and congruences

@article{Tilouine2022IntegralPR,
title={Integral period relations and congruences},
author={Jacques Tilouine and Eric Urban},
journal={Algebra \&amp; Number Theory},
year={2022}
}
• Published 27 November 2018
• Mathematics
• Algebra &amp; Number Theory
Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida regarding the {\it congruence number} controlling the congruences between this base change and other eigenforms which are not base change. As a corollary, we establish the Bloch-Kato conjecture for adjoint modular Galois representations twisted by an even quadratic character. In the odd case, we…
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