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Relates invariants of a curve defined over the Integers. If this inequality were proven true, then Fermat's Last Theorem would follow for sufficiently large exponents. Miyaoka claimed to have proven this inequality in 1988, but the proof contained an error.
See also Fermat's Last Theorem
References
Cox, D. A. ``Introduction to Fermat's Last Theorem.'' Amer. Math. Monthly 101, 3-14, 1994.