Van den Essen's theorem on the de Rham cohomology of a holonomic\n D-module over a formal power series ring

2015/05/07 by Nicholas Switala, Switala, Nicholas · 1 citation
Mathematics · #14F40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 14F10

paper · pdf · doi:10.48550/arxiv.1505.01788

openalex publication_date 2015/05/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this expository paper, we give a complete proof of van den Essen's theorem\nthat the de Rham cohomology spaces of a holonomic D-module are\nfinite-dimensional in the case of a formal power series ring over a field of\ncharacteristic zero. This proof requires results from at least five of van den\nEssen's papers as well as his unpublished thesis, and until now has not been\navailable in a self-contained document.\n

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