{"id":"openai-math/Tame-Hecke-Eigensheaves-with-Several-Marked-Points","pdf":"https://github.com/openai/math/blob/main/preprints/Tame-Hecke-Eigensheaves-with-Several-Marked-Points-October-5-2026/Tame-Hecke-Eigensheaves-with-Several-Marked-Points.pdf","url":"https://github.com/openai/math/tree/main/preprints/Tame-Hecke-Eigensheaves-with-Several-Marked-Points-October-5-2026","tags":["geometric-langlands","hecke-eigensheaves","algebraic-geometry"],"score":0,"title":"Tame Hecke Eigensheaves with Several Marked Points","domain":"Number theory","family":"014","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"For SL n in characteristic p > n , we construct nonzero locally constructible perverse Hecke eigensheaves with Borel level at two or more marked points on a smooth projective curve of genus at least two over an algebraic closure of a finite field. The parameter is a Zariski-dense geometric ℓ -adic PGL n -local system with unipotent tame monodromy; its nilpotent logarithms may have any Jordan type, including zero. The eigensheaves have parabolic nilpotent singular support, and their eigenisomorphisms retain the full tensor and fusion structure.","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"}