{"id":"openai-math/Constructible-tame-Hecke-eigensheaves-in-positive-characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Constructible-tame-Hecke-eigensheaves-in-positive-characteristic-October-5-2026/constructible-tame-hecke-eigensheaves-positive-characteristic.pdf","url":"https://github.com/openai/math/tree/main/preprints/Constructible-tame-Hecke-eigensheaves-in-positive-characteristic-October-5-2026","tags":["langlands-program","number-theory","algebraic-geometry"],"score":0,"title":"Constructible tame Hecke eigensheaves in positive characteristic","domain":"Number theory","family":"014","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We construct nonzero locally constructible perverse Hecke eigensheaves with Borel level at one marked point 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 local system with tame regular-unipotent monodromy. The group is simple and simply connected and satisfies four explicit Lie-theoretic characteristic hypotheses. The eigensheaves have parabolic nilpotent singular support, and their eigenisomorphisms are compatible with tensor products, permutations, and fusion.","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"}