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math.NT2025
-retract Rationality and Norm One Tori
Kazuki Sato
We study whether the norm one torus associated with a finite separable non-Galois field extension is -retract rational over for a prime , focusing on the case where…
math.NT2014
Rational Points on Diagonal Cubic Surfaces
Kazuki Sato
We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p…
math.NT2013
Hasse principle for the Chow groups on quadric fibrations
Kazuki Sato
We give a sufficient condition for the injectivity of the global-to-local map of the relative Chow group of zero-cycles on a quadric fibration of dimension 2 or 3 defined over a nu…