I find this quote in Martin Krieger, Doing Mathematics: Convention, Subject, Calculation, Analogy, New Jersey, World Scientific Publishing, 2003, p. 223.
"Hilbert then shows how one of Dedekind's notions of a prime factor or ideal (the different) corresponds to the Riemann-Roch theorem, a geometric and arithmetic fact concerning the topology of Riemann's surfaces."
Could anyone explain it to me in some not too tecnical detail? What does "the different" mean in that context?