Scientists / Open questions
André Weil
Number theory; algebraic geometry
7 questions
Unboundedness and effective computation of the Mordell–Weil rank of curves over a fixed number field (the open questions of Weil's 1929 'L'arithmétique sur les courbes algébriques')
Manifold structure of the connected components of Weil's space of faithful discrete cocompact representations
The defect term in Weil's 1935 Riemann-Roch formula for automorphic differential vectors: behavior for multiplier systems with infinite image
Weil's 1947 question: must an integral Kähler class be homologous to a positive analytic cycle?
The undetermined algebraic factors in Weil's period formula for Fermat-type curves: the exact multipliers, their number fields, denominators, and p-adic properties
The modular case of Weil's cohomology dimension formula for Fuchsian orbifold groups: characteristic dividing an elliptic generator order
Weil's closing question of Chapter II (1964): a proof of the general reciprocity law of class field theory analogous to the metaplectic proof of quadratic reciprocity