de Rham-Witt上同调中的高维多米诺
Higher dimensional dominoes in de Rham-Witt cohomology
AI总结：
本文对de Rham-Witt上同调中的二维多米诺分类，将任意维多米诺标准化，赋予其两个幂幺群并证明同源划分一致，还计算超奇异阿贝尔簇多米诺、界定Brauer群指数，解答了相关问题。
AI中文摘要：
特征p下光滑真概形的de Rham-Witt上同调包含一个称为多米诺的典范分支，它在Witt向量上不是有限生成的，且承载着斜率谱序列的非零微分。除一维情况外，多米诺尚未被分类。我们对二维多米诺进行分类，并将任意维数的多米诺化为标准型。对每个多米诺，我们赋予其两个幂幺群：一个形式幂幺群和一个完美幂幺群，证明它们的同源划分一致。在二维情形，我们从Mazur-Ogus概形的晶态上同调中恢复其多米诺，计算两类超奇异阿贝尔簇的多米诺，并对每个素数p，用a-数界定p-主Brauer群的指数，回答了Grammatica-Skorobogatov-Yang提出的问题。
英文摘要：
The de Rham-Witt cohomology of a smooth proper variety in characteristic $p$ contains a canonical piece called the domino, which is not finitely generated over the Witt vectors and carries the nonzero differentials of the slope spectral sequence. Beyond dimension one, dominoes were unclassified. We classify the two-dimensional ones and put a domino of any dimension into a normal form. To each domino we attach two unipotent groups, one formal and one perfect, and prove that their isogeny partitions agree. In degree two we recover the domino of a Mazur-Ogus variety from its crystalline cohomology, compute it for two families of supersingular abelian varieties, and bound the exponent of the $p$-primary Brauer group in terms of the $a$-number, for every prime $p$. This answers a question of Grammatica-Skorobogatov-Yang.
