An analogue of Ogus’s theorem for certain hypergeometric curves

For a family whose Picard–Fuchs equation is given by a certain hypergeometric differential equation, we express the Frobenius action on the de Rham cohomology as products of p-adic gamma values. Such an expression is known in specific cases, namely Fermat curves and CM elliptic curves, but remains unknown in general. The main result of this paper provides new examples. The idea of the proof is to reduce the statement to the case of CM elliptic curves by using a transformation formula for hypergeometric functions.