半阿贝尔雅可比簇的Chai猜想
Chai's conjecture for semiabelian Jacobians
AI总结：
本文证明Chai关于半阿贝尔簇基变换导子可加性的猜想在正常曲线雅可比簇情形成立，推广了Raynaud构造，并证明了完美剩余域下Néron模型存在性的两个猜想。
摘要：
我们证明了Chai关于半阿贝尔簇基变换导子可加性的猜想在正常曲线雅可比簇情形下的成立。这包括第一个非平凡狂野分歧的无限族例子。在此过程中，我们将Raynaud基于Picard函子构造雅可比簇Néron lft-模型的方法推广到任意半正规曲线（超出此范围，雅可比簇不存在Néron lft-模型，正如我们更一般的结构结果所示）。最后，我们研究了在不完备度至多为一的域上（不一定几何约化的）正常曲线雅可比簇的结构，并证明了Bosch-Lütkebohmert-Raynaud关于一般正常曲线雅可比簇在完美剩余域情形下Néron模型和Néron lft-模型存在性的两个猜想，从而加强了作者此前在该情形下的结果。
英文摘要：
We prove Chai's conjecture on the additivity of the base change conductor of semiabelian varieties in the case of Jacobians of proper curves. This includes the first infinite family of non-trivial wildly ramified examples. Along the way, we extend Raynaud's construction of the Néron lft-model of a Jacobian in terms of the Picard functor to arbitrary seminormal curves (beyond which Jacobians admit no Néron lft-models, as shown by our more general structural results). Finally, we investigate the structure of Jacobians of (not necessarily geometrically reduced) proper curves over fields of degree of imperfection at most one and prove two conjectures about the existence of Néron models and Néron lft-models due to Bosch-Lütkebohmert-Raynaud for Jacobians of general proper curves in the case of perfect residue fields, thus strengthening the author's previous results in this situation.
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