Non-critical equivariant L-values of modular abelian varieties
  We prove an equivariant version of Beilinson's conjecture on non-critical $L$-values of strongly modular abelian varieties over number fields. As an application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and Deninger's conjecture on $L(E,3)$ for non-CM strongly modular $\mathbf{Q}$-curves. 
Fran\c{c}ois Brunault
math.NT math.AG