论文标题
特征2尖锐球的各向异性
The characteristic 2 anisotropicity of simplicial spheres
论文作者
论文摘要
假设D是一个简单的球体，而K_1是一个字段。我们说，d在K_1上通常是各向异性的，如果对于K_1的某些纯粹的先验场扩展k，则某些stanley-reisner ring k [d]具有以下属性：所有非零同质元素的a均具有以下属性：a。我们证明，使用合适的微分运算符，如果字段K_1具有特征2，则每个Simplicial Sphere D在K_1上都是各向异性的。作为一种应用，我们给出了第二个证明脂肪片的最新结果，称为麦克穆伦（McMullen）的G-conjocture用于简单球。我们还证明，在任何字段K_1上，维度1的简单球通常是各向异性的。
Assume D is a simplicial sphere, and k_1 is a field. We say that D is generically anisotropic over k_1 if, for a certain purely transcendental field extension k of k_1, 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 k_1 has characteristic 2, then every simplicial sphere D is generically anisotropic over k_1. 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 k_1.
