# Integral period relations and congruences

@article{Tilouine2022IntegralPR, title={Integral period relations and congruences}, author={Jacques Tilouine and Eric Urban}, journal={Algebra \& Number Theory}, year={2022} }

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…

## 6 Citations

Iwasawa theory for quadratic Hilbert modular forms

- Mathematics
- 2020

We study the Iwasawa main conjecture for quadratic Hilbert modular forms over the p-cyclotomic tower. Using an Euler system in the cohomology of Siegel modular varieties, we prove the "Kato…

Twisted adjoint L-values, dihedral congruence primes and the Bloch–Kato conjecture

- Mathematics
- 2020

We show that a dihedral congruence prime for a normalised Hecke eigenform f in
$$S_k(\Gamma _0(D),\chi _D)$$
, where
$$\chi _D$$
is a real quadratic character, appears in the denominator of the…

Overconvergent cohomology, p-adic L-functions and families for GL(2) over CM fields

- MathematicsJournal de Théorie des Nombres de Bordeaux
- 2022

The study of overconvergent cohomology, initiated by Pollack and Stevens in the setting of classical modular forms, has now been used to construct p-adic L-functions in a number of settings. The…

p-adic L-functions for non-critical adjoint L-values

- Mathematics
- 2019

Let $K$ be an imaginary quadratic field, with associated quadratic character $\alpha$. We construct an analytic $p$-adic $L$-function interpolating the twisted adjoint $L$-values $L(1, \mathrm{ad}(f)…

Special L-values and Selmer groups of Siegel modular forms of genus 2

- Mathematics
- 2018

Let $p$ be an odd prime, $N$ a square-free odd positive integer prime to $p$, $\pi$ a $p$-ordinary cohomological irreducible cuspidal automorphic representation of…

Wiles defect for Hecke algebras that are not complete intersections

- MathematicsCompositio Mathematica
- 2021

In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings $R\to T$ to be an isomorphism of complete intersections. He used this to show that certain deformation rings…

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