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We compute periods of perturbations of a Fermat variety. This allows us toconsider a subspace of the Hodge cycles defined by "simple" arithmeticconditions. We explore some examples and give an upper bound for the dimensionof this subspace. As an application, we find explicit expressions involvingsome Gauss' hypergeometric functions which are algebraic over the field ofrational functions in one variable.

Periods of Hodge cycles and special values of the Gauss' hypergeometric function