We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to a Hilbert modular form under mild assumptions on the residual image. In particular, we do not assume the residual image satisfies the Taylor–Wiles hypothesis. Using this, we deduce that the localization and completion of the universal deformation ring for the r...

We have previously modeled the Doctrine of Double Effect (DDE) in a formal computational logic [1]. While DDE can account for a large range of human behavior in moral dilemmas (situations in which all available actions have positive and negative effects), the doctrines have to be further extended to account for how humans behave (and ought to behave). One such extension has produced a version o...

Consider the smooth projective models C of curves y = f(x) with f(x) ∈ Z[x] monic and separable of degree 2g + 1. We prove that for g ≥ 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower bound on this fraction that tends to 1 as g → ∞. Finally, we show that C(Q) can be algorithmically computed for such a fraction of the curves. The method can b...