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Results tagged with modular-forms
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user 6121
Questions about modular forms and related areas
17
votes
1
answer
2k
views
Construction of abelian varieties from Hilbert modular forms?
Some experts tell me that the construction of abelian varieties from
Hilbert modular forms is an (apparently difficult) open problem. However,
in view of the construction of $l$-adic Galois representa …
- 1,141
7
votes
Nonvanishing of central L-values of quadratic twists?
Though it is perhaps not an "answer" as such, let me try to explain some intuition.
In certain settings, it is possible to formulate subtle analogues of Mazur's conjecture
for nonvanishing of central …
- 1,141
7
votes
1
answer
1k
views
Status of Ihara's lemma for Shimura curves over totally real fields?
What is the status of Ihara's lemma for Shimura curves over totally real fields?
In particular, why is it not implicit in the exact sequence of Rajaei, "On the levels of mod $l$ Hilbert modular forms" …
- 1,141
3
votes
What do we know about the structure of $J_{0}(N)$ over $\mathbb{Q}[{\mu}_{{p}^{\infty}},{{k}...
The case of Kummer extensions is not yet completely understood, though partial results are obtained by Darmon-Tian in "Heegner points over towers of Kummer Extensions", Canad. J. Math. 62 (5) 2010, 10 …
- 1,141
3
votes
Accepted
Status of Ihara's lemma for Shimura curves over totally real fields?
Okay, so the answer to the naive question is most likely no for several reasons. For instance, the identifications explained in the second paragraph show that the injection in Rajaei is really an anal …
- 1,141