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Integral period relations and the Blochâ Kato formula for quadratic twists of the adjoint L-function

Banff International Research Station for Mathematical Innovation and Discovery

In a joint work with E. Urban, we prove under mild assumptions Integral Period Re- lations for the quadratic base change of a modular form and we compute the relative congruence number in terms of the value at s = 1 of a quadratic twist of the adjoint L-function. This proves a conjecture of Hida (1999). It also implies, under standard Taylor-Wiles type assumptions, in the real quadratic case, resp. in the imaginary quadratic case, the Bloch-Kato formula, resp. an analogue of it. This analogue would be the exact conjectural Bloch-Kato formula if a Bianchi period defined by E. Urban in his thesis could be related to a Bloch-Kato-Beilinson regulator.
<br/> Related references: <br/> S. Bloch, K. Kato: Grothendieck Festschrift vol I, Birkhauser pp 333-400, 1990
<br/> H. Hida: Non-critical values of adjoint L-functions for SL(2), Proc. Symp. Pure Math. 66 (1999) Part I, 123-175

Mathematics; Number theory; Algebraic geometry; Arithmetic number theory

video/mp4

Author affiliation: Université Paris 13

2019-03-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69360

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/