2020/12/17 by Stavros Argyrios Papadakis, Papadakis, Stavros Argyrios, Vasiliki Petrotou +1 · 4 citations
Mathematics · #05E45 #11R58 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 13F55 #Secondary 05E40
paper · pdf · doi:10.48550/arxiv.2012.09815
openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume D is a simplicial sphere, and k1 is a field. We say that D is generically anisotropic over k1 if, for a certain purely transcendental field extension k of k1, a certain Artinian reduction A of the Stanley-Reisner ring k[D] has the following property: All nonzero homogeneous elements u of A of degree less or equal to (dim D +1)/2 have nonzero square. We prove, using suitable differential operators, that, if the field k1 has characteristic 2, then every simplicial sphere D is generically anisotropic over k1. As an application, we give a second proof of a recent result of Adiprasito, known as McMullen's g-conjecture for simplicial spheres. We also prove that the simplicial spheres of dimension 1 are generically anisotropic over any field k1.