2019/09/14 by Arpan Dutta, Dutta, Arpan
Computer Science · Mathematics · #12J20 #12J25 #13A18 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1909.06546
openalex publication_date 2019/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abhyankar showed that for a finite tame extension L1/K and a finite extension L2/K of \mathfrakP-adic fields, the condition [νL1 : νK] divides [νL2 : νK] is sufficient to eliminate ramification, that is, L1 ⋅ L2 / L2 is unramified. In this paper, we show that the above condition is not sufficient in the case of an arbitrary henselian valued field. We construct a counterexample illustrating that fact. We also give a necessary and sufficient condition for the elimination of tame ramification of a henselian field after a finite extension of the base field.