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A basis of algebraic de Rham cohomology of complete intersections over a characteristic zero field
Let k be a field of characteristic 0. Let X be a smooth complete intersection over k of dimension n − k in the projective space P k , for given positive integers n and k. When k = C, Terasoma ([10])Expand
A homotopy Lie formula for the p-adic Dwork Frobenius operator
We give a modern deformation theoretic interpretation of Dwork's theory of the zeta function of a smooth projective complete intersection variety $X$ over a finite field. Using this interpretation,Expand
An algorithm for a Massey triple product of a smooth projective plane curve
We provide an explicit algorithm to compute a Massey triple product relative to a defining system for a smooth projective plane curve $X$ defined by a homogeneous polynomial $G(\underline x)$ over aExpand
Polynomial realizations of period matrices of projective smooth complete intersections and their deformation
Let X be a smooth complete intersection over C of dimension n − k in the projective space P n C , for given positive integers n and k. For a given integral homology cycle [γ] ∈ Hn−k(X(C), Z), theExpand
On the Jacobian of hyperelliptic curves $y^2 = x^5 + m^2$
In this paper, we study the algebraic rank and the analytic rank of the Jacobian of hyperelliptic curves y = x + m for integers m. Namely, we first provide a condition on m that gives a bound of theExpand