{"id":"openai-math/Frobenius-Structures-on-Tame-Hecke-Eigensheaves","pdf":"https://github.com/openai/math/blob/main/preprints/Frobenius-Structures-on-Tame-Hecke-Eigensheaves-October-5-2026/tame-hecke-frobenius.pdf","url":"https://github.com/openai/math/tree/main/preprints/Frobenius-Structures-on-Tame-Hecke-Eigensheaves-October-5-2026","tags":["representation-theory","geometric-langlands","perverse-sheaves"],"score":0,"title":"Frobenius Structures on Tame Hecke Eigensheaves","domain":"Number theory","family":"014","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We construct nonzero perverse Weil Hecke eigensheaves for SL n with Borel level at one marked point, after a finite extension of the field of constants. The parameter is a geometrically dense arithmetic PGL n -local system with tame regular-unipotent monodromy on a once-punctured curve of genus at least two over a finite field of characteristic p > n . The full multi-leg eigenstructure is Frobenius compatible with the prescribed arithmetic eigenvalue, and the geometric sheaf has parabolic nilpotent singular support.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan"}