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I have the following naive (and inexpert) question about the reduction of Shimura curves at primes dividing the discriminant of the underlying quaternion algebra. It requires some background to state. …

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 …

Is it not possible to prove mutiplicity one type statements for character groups of quaternionic Shimura curves by simply using Raynaud's description for character groups at primes dividing the underl …

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" …

I think the general wisdom is that Deligne's Travaux de Shimura and Milne's Introduction to Shimura Varieties are the most comprehensive references, with the latter being somewhat lighter on prerequis …

Is there any (conjectural) characterization of $\overline{\bf{Q}}$-points on Shimura varieties? The question of course does not always make sense for ${\bf{Q}}$-points: a theorem of Shimura shows th …

What is the precise relationship between the Selmer group of an abelian variety and that of its dual? For instance, does the vanishing of one not imply the same for the other? To fix ideas, let $A$ …

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 …