Submission date: 2 June 2024

Abstract:

We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a difference variety in terms of its transformal dimension. As a main technical ingredient, we prove an equidimensionality result for Frobenius reductions of difference varieties.

Mathematics Subject Classification: Primary 12H10, 11U09 Secondary 03C60, 03C20 \\

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Full text arXiv 2406.00880: pdf, ps.