论文标题
特征$ p \ geq 5 $的泰特猜想甚至是尺寸的gushel-mukai品种
The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic $p\geq 5$
论文作者
论文摘要
我们研究了特征$ p $的尺寸4或6的Gushel-Mukai（GM）品种。我们的主要结果是在有限生成的特征$ p \ geq 5 $的有限生成的字段上的所有这些品种的泰特猜想。对于GM六倍，我们遵循Madapusi Pera使用的方法，证明了K3表面的泰特猜想。作为此的输入，我们证明了有关GM六倍的许多基本结果，例如没有非零的全局向量字段。对于转基因四倍，我们通过利用广义伙伴的概念以及特征性0中的广义伙伴在中等程度上具有同构的CHOW动机，从而证明了泰特猜想的猜想。证明的几个步骤取决于特征0的结果，这些结果被证明了我们的论文“ Gushel-Mukai品种上的代数周期”，épijournalgéométriealgbrique，卷spécialen l'honneur de claire de claire voisin，2024年。
We study Gushel-Mukai (GM) varieties of dimension 4 or 6 in characteristic $p$. Our main result is the Tate conjecture for all such varieties over finitely generated fields of characteristic $p\geq 5$. In the case of GM sixfolds, we follow the method used by Madapusi Pera in his proof of the Tate conjecture for K3 surfaces. As input for this, we prove a number of basic results about GM sixfolds, such as the fact that there are no nonzero global vector fields. For GM fourfolds, we prove the Tate conjecture by reducing it to the case of GM sixfolds by making use of the notion of generalised partners plus the fact that generalised partners in characteristic 0 have isomorphic Chow motives in the middle degree. Several steps in the proofs rely on results in characteristic 0 that are proven our paper "Algebraic cycles on Gushel-Mukai varieties", Épijournal Géométrie Algébrique, Volume spécial en l'honneur de Claire Voisin, 2024.
