{"id":"openai-math/Integral-points-on-character-varieties-of-curves","pdf":"https://github.com/openai/math/blob/main/preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Integral-points-on-character-varieties-of-curves-September-25-2026","tags":["arithmetic-geometry","character-varieties","representation-theory"],"score":0,"title":"Integral points on character varieties of curves","domain":"Number theory","family":"027","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove potential Zariski density of integral points on SL r -character varieties of smooth complex curves in every rank. The result allows prescribed quasi-unipotent boundary monodromy, including exact nonsemisimple conjugacy classes, and holds on every component over the full ring of integers of one finite extension. Here integrality is measured in the ambient character variety, while the exact boundary conditions are imposed on the complex representation.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Potential integral density on curve character varieties"}