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The aim is to create a discretized framework for the Langlands program specifically for characteristic p function fields.

April 7, 2026Open Access

Arithmetic Discrete Geometry and the Langlands Program: A Limit Approximation Approach in Characteristic p

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The aim is to create a discretized framework for the Langlands program specifically for characteristic p function fields.
Developed equipped graphs as combinatorial models for algebraic curves.
Defined discrete valuation rings and local fields to establish theoretical foundations.
Constructed discrete moduli stacks for G-bundles and local systems on single-loop graphs.
Introduced an algorithmic approach to approximate Frobenius traces for efficient L-function computations.
Established a categorical equivalence conjecture between the moduli stack and the local system stack.
Verified discrete geometric Satake equivalence for G = SL(2).
Provided a new computability pathway for characteristic p Langlands correspondence.

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Constructs a discretized Langlands theory for function fields, suggesting new computational paths.

Jianming wang (2026) studied this question.

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