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math.NT2026
Factorizations of linearized polynomials and extremal curves in odd characteristic
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
We give a complete recipe for constructing extremal van der Geer--van der Vlugt curves over finite fields of odd characteristic. The input data consist of a nonzero element of the…
math.NT2026
Factorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2
Tetsushi Ito, Daichi Takeuchi, Takahiro Tsushima
In our previous work, we gave a formula for the Frobenius eigenvalues of van der Geer--van der Vlugt curves in characteristic 2 by considering suitable quotients of the curve. Alth…
math.AG2026
Bernstein--Sato Theory for D-modules in Positive Characteristic
Daichi Takeuchi
In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian…