p-adic Gelfand-Kapranov-Zelevinsky systems

par Lei Fu (Yau Mathematical Sciences Center, Tsinghua University)

mercredi 16 janv. 2019, 10:00 → 11:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Using Dwork’s trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of $D^{\dagger}$-modules with Frobenius structure.