Abstract
We study the number of rational points of smooth projective curves over finite fields in some situations in the spirit of a previous paper [HP19] from an euclidean point of vue. We prove some kinds of Weil bounds, derived from Schwarz inequality for some relative parts of the diagonal and of the graph of the Frobenius on some euclidean sub-spaces of the numerical space of the squared curve endowed with the opposite of the intersection product.
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