论文标题
伪 - 阿贝尔品种的néron模型
Néron models of pseudo-Abelian varieties
论文作者
论文摘要
我们研究了伪 - 亚伯式品种的Néron模型，这是在具有均等特征$ p> 0 $的出色离散估值环上，并概括了良好的减少和Semiabelian还原的概念。我们证明，由于Néron-Ogg-Shafarevich和Grothendieck而导致的良好和半阳离子降低的众所周知的代表性理论标准延续到了伪 - 亚伯利亚案件中，并举例说明我们的结果在大多数情况下都是最好的。最后，我们研究了伪 - 阿贝尔案中Néron模型连接组件的组方案的顺序。我们的方法能够完全控制该订单的$ \ ell $ -part（对于$ \ ell \ not = p $），并且我们在特定（但仍然相当普遍）的情况下研究了$ p $ - 部分。
We study Néron models of pseudo-Abelian varieties over excellent discrete valuation rings of equal characteristic $p>0$ and generalize the notions of good reduction and semiabelian reduction to such algebraic groups. We prove that the well-known representation-theoretic criteria for good and semiabelian reduction due to Néron-Ogg-Shafarevich and Grothendieck carry over to the pseudo-Abelian case, and give examples to show that our results are the best possible in most cases. Finally, we study the order of the group scheme of connected components of the Néron model in the pseudo-Abelian case. Our method is able to control the $\ell$-part (for $\ell\not=p$) of this order completely, and we study the $p$-part in a particular (but still reasonably general) situation.
