Year: 2025
Type: article
Abstract: Let p≥3 be a prime number. A Fermat curve over Q of exponent p is defined by an equation of the form axp+byp+czp=0, where a, b, c are non-zero rational numbers. We prove in this article that there exist infinitely many Fermat curves defined over Q, of exponent p, pairwise non Q-isomorphic, contradicting the Hasse principle.
Source: Acta Arithmetica
DOI: 10.4064/aa250111-4-8
Author: Alain Kraus
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4414936252
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