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arxiv: 1206.4039 · v3 · pith:FELJ3MG5new · submitted 2012-06-18 · 🧮 math.AG · math.AC

The Lemma on b-functions in Positive Characteristic

Theodore J. Stadnik Jr This is my paper
classification 🧮 math.AG math.AC
keywords finitelocallyarticleb-functionscharacteristicdeterminedequippedessentially
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Let $X$ be an $F$-finite smooth scheme of essentially finite type over a perfect field. This article proves the existence of $b$-functions for locally finitely generated unit $F$-modules when equipped with their induced $\mathbb{D}_X$-module structure. It is shown that the $b$-function has rational roots and is determined locally in the \'etale topology.

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  1. Bernstein--Sato Theory for D-modules in Positive Characteristic

    math.AG 2026-04 unverdicted novelty 7.0

    Defines Bernstein-Sato roots for D-modules in positive characteristic as p-adic integers and proves they are finite and rational for locally finitely generated unit F^e-modules on finite type schemes over F-finite fields.