AI 中文总结
本文证明特征正完美域上连通几何单枝簇的过收敛等晶体范畴Tannaka对偶间典范同态为商映射，而收敛等晶体及所有等晶体的类似命题不成立，反例基于Crew的单位根F-等晶体构造。
AI 中文摘要
我们证明：在特征为正的完美域上，连通几何单枝簇X及稠密开子集U⊂X上，过收敛等晶体范畴的Tannaka对偶间的典范同态是商映射。同时表明，收敛等晶体及所有等晶体的类似命题不成立，反例基于Crew构造的收敛但非过收敛的单位根F-等晶体。
英文摘要
We prove that for a connected, geometrically unibranch variety $X$ over a perfect field of positive characteristic and a dense open subset $U \subset X$, the canonical homomorphism between the Tannaka duals of the categories of overconvergent isocrystals is a quotient map. We also show that the analogous statement for convergent isocrystals, and for all isocrystals, fails. The counterexample is based on Crew's construction of a unit-root $F$-isocrystal that is convergent but not overconvergent.
