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Frobenius Structures on Tame Hecke Eigensheaves

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OpenAI Mathopenai-math/Frobenius-Structures-on-Tame-Hecke-EigensheavesOct 5, 2026math.NTAI-generatedscore 0

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.

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