论文标题
卡地亚代数的卡地亚核心地图
The Cartier core map for Cartier algebras
论文作者
论文摘要
令$ r $为$ f $ f $ f $ finite的主要特征戒指，让$ \ mathcal {d} $成为卡地亚代数。我们通过将点$ P $发送到$（R_P，\ Mathcal {d} _p）$的分裂plime来定义$（R，\ Mathcal {d}）$的Frobenius拆分基因座上的自图。我们证明这张地图是连续的，保存的，并修复了$ \ Mathcal {d} $ - 兼容的理想。我们显示该地图可以扩展到任意理想$ J $，在Frobenius Split Case中，它提供了最大的$ \ Mathcal {d} $ - 兼容$ J $中包含的理想。最后，我们采用Glassbrenner的标准来证明斯坦利 - 里亚人戒指的统一理想是其最少的素数的总和。
Let $R$ be a commutative Noetherian $F$-finite ring of prime characteristic and let $\mathcal{D}$ be a Cartier algebra. We define a self-map on the Frobenius split locus of the pair $(R,\mathcal{D})$ by sending a point $P$ to the splitting prime of $(R_P, \mathcal{D}_P)$. We prove this map is continuous, containment preserving, and fixes the $\mathcal{D}$-compatible ideals. We show this map can be extended to arbitrary ideals $J$, where in the Frobenius split case it gives the largest $\mathcal{D}$-compatible ideal contained in $J$. Finally, we apply Glassbrenner's criterion to prove that the prime uniformly $F$-compatible ideals of a Stanley-Reisner rings are the sums of its minimal primes.
