{"id":"hexagon/2611.00071","pdf":"https://hexagonmath.org/pdf/2611.00071v1","url":"https://hexagonmath.org/abs/2611.00071v1","tags":["msc:11F80","Galois representations","Serre conjecture","quadratic fields"],"score":0,"title":"Serre modularity over real quadratic fields","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Luis V. Dieulefait","Nuno Freitas","Ariel Pacetti"],"reviews":0,"subject":"math.NT","summary":"Assuming GRH for Dedekind zeta functions, we prove Serre’s conjecture over the real quadratic fields \\(\\mathbf Q(\\sqrt d)\\) for \\[ d\\in\\{2,3,5,6,7,10,11,13,17,21,33,37,41,57,65,73,89\\}. \\] More precisely, every continuous, absolutely irreducible, totally odd two-dimensional Galois representation over these fields in odd residual characteristic is modular. The result for \\(d=17\\) is unconditional; for \\(d=33\\), GRH can be replaced by the assertion that Dedekind zeta functions have no zeros with real part greater than \\(31/32\\). The proof combines conductor reduction with local ramification…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}