Speaker
Eleonora Svanberg
Description
For the one-parameter mirror quintic Calabi–Yau threefold, we derive an explicit formula for the point count over F_p in terms of a p-adic expansion involving only the periods of the holomorphic (3,0)-form. The period basis is obtained via the Frobenius method, and after a suitable change of basis, the expansion naturally incorporates p-adic zeta values. This result establishes a direct arithmetic–geometric link between point counting and period integrals. If time permits, we will discuss extensions to F_q and the five-parameter Hulek–Verrill manifold.
