同源晶格的潜在平凡性与真覆盖
Potential isotriviality of isocrystals and proper covers
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中文总结 AI 辅助
本文研究同源晶格在真覆盖拉回后变为平凡的条件，证明在几何单分支簇上可由有限平展覆盖实现，并蕴含几何单值群有限性，同时以结点曲线说明假设必要性。
中文摘要 AI 辅助
我们研究在真满射态射拉回后变为平凡态的收敛和超收敛同源晶格。在代数闭域上的几何单分支簇上，每个此类对象都已被有限平展覆盖平凡化。在完美域上，这表明给出几何平凡性的真覆盖可以被地面域上的有限平展覆盖所替代，并蕴含几何单值群的有限性。对于真几何单分支簇，有限几何单值也是充分的。在超收敛情形中，一个支配态射可以替代给定的真覆盖。一个结点曲线说明了为何需要几何单分支假设。
英文摘要
We study convergent and overconvergent isocrystals that become trivial after pullback along a proper surjective morphism. On a geometrically unibranch variety over an algebraically closed field, every such object is already trivialized by a finite étale cover. Over a perfect field, this shows that a proper cover giving geometric triviality can be replaced by a finite étale cover over the ground field, and implies finiteness of the geometric monodromy group. For proper geometrically unibranch varieties, finite geometric monodromy is also sufficient. In the overconvergent case, a dominant morphism can replace the given proper cover. A nodal curve shows why the geometrically unibranch hypothesis is needed.
发表机构
- University of Warsaw, Institute of Mathematics（华沙大学数学研究所）
- Sun Yat-Sen University School of Mathematics (Zhuhai)（中山大学数学学院（珠海））
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