Scientists / Open questions
Jean-Pierre Serre
Algebraic geometry; number theory; topology
1954 Fields Medal
29 questions
Small normalized discriminants for non-solvable Galois extensions of ramified at a single prime: extending the Dembélé–Serre analysis beyond
Open questions from Serre's 'Quelques applications du théorème de densité de Chebotarev' (1981): Frobenius counting on thin sets, removal of GRH, Serre's uniformity problem, lacunarity of Fourier coefficients, and the Lang–Trotter asymptotic
Serre's 1971 cohomology program for discrete and S-arithmetic groups: finiteness properties, Euler-Poincare characteristics, analytic versus continuous cohomology of p-adic groups, and integrality of zeta values
Serre's 1951 problem on fibrations of Euclidean space with connected fibres: the triviality question
Sharp convergence domain of the Campbell–Hausdorff series over the real and complex numbers