Galois-invariant Néron--Severi ranks of Fermat surfaces over number fields: a Galois module, closed forms, a threshold, and exact tables

Rifat Jumagulov

For a Fermat surface X_d: x_0^d+x_1^d+x_2^d+x_3^d=0 we compute the Galois-invariant Neron-Severi (Picard) rank rho_K(X_d) = dim (NS(X) \otimes Q)^{Gal(Qbar/K)}: for every subfield…