Cohen–Lenstra heuristics for étale group schemes and symplectic pairings
Cohen–Lenstra heuristics for étale group schemes and symplectic pairings
We generalize the Cohen–Lenstra heuristics over function fields to étale group schemes $G$ (with the classical case of abelian groups corresponding to constant group schemes). By using the results of Ellenberg–Venkatesh–Westerland, we make progress towards the proof of these heuristics. Moreover, by keeping track of the image of the Weil-pairing …