对数 Hodge 模空间的几何（与 Siqing Zhang 合著的附录）
Geometry of the logarithmic Hodge moduli space (with an Appendix joint with Siqing Zhang)
AI总结：
本文证明了对数 t-连接的 Hodge 模空间及其相关模空间在仿射直线上的光滑性与几何整性，并利用光滑性导出其平展上同调环的特殊化同构，证明了在正特征可分闭域情形下这些同构是反常层滤过的滤过同构。
摘要：
我们证明：在任意 Noetherian 基上，对于光滑射影曲线上秩与次数互素的对数 t-连接的 Hodge 模空间，其在仿射直线上的光滑性，且其几何纤维是几何整的。当基是域时，我们还证明该 Hodge 模空间是几何整的。在此过程中，我们对相应的对数 Higgs 从模空间和对数连接模空间证明了相同的结果。我们利用光滑性导出这些模空间平展上同调环上的特殊化同构；这包含基为混合特征的特殊情形。在基为正特征的 separably closed 域的特殊情形下，我们证明这些同构对于相应 Hitchin 型态射关联的反常层滤过是滤过同构。
英文摘要：
We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base is a field, we also prove that the Hodge moduli space is geometrically integral. Along the way, we prove the same results for the corresponding moduli spaces of logarithmic Higgs bundles and of logarithmic connections. We use smoothness to derive specialization isomorphisms on the etale cohomology rings of these moduli spaces; this includes the special case when the base is of mixed characteristic. In the special case where the base is a separably closed field of positive characteristic, we show that these isomorphisms are filtered isomorphisms for the perverse filtrations associated with the corresponding Hitchin-type morphisms.
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