2012/08/27 by Wouter Castryck, Castryck, Wouter, Robert Laterveer +4
Mathematics · #12D10 #14-04 #14XX #30C15 #30E99 #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:12D10 #msc:14-04 #msc:14XX #msc:30C15 #msc:30E99
paper · pdf · doi:10.48550/arxiv.1208.5404
arxiv created 2012/08/27 · openalex publication_date 2012/08/27 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a first (theoretical) part of this paper, we prove a number of constraints on hypothetical counterexamples to the Casas-Alvero conjecture, building on ideas of Graf von Bothmer, Labs, Schicho and van de Woestijne that were recently reinterpreted by Draisma and de Jong in terms of p-adic valuations. In a second (computational) part, we present ideas improving upon Diaz-Toca and Gonzalez-Vega's Gröbner basis approach to the Casas-Alvero conjecture. One application is an extension of the proof of Graf von Bothmer et al. to the cases 5pk, 6pk and 7pk (that is, for each of these cases, we elaborate the finite list of primes p for which their proof is not applicable). Finally, by combining both parts, we settle the Casas-Alvero conjecture in degree 12 (the smallest open case).