无Frobenius结构的完全忠实性和部分过相干等晶
Full faithfulness without Frobenius structure and partially overcoherent isocrystals
摘要：
设$K$是具有完美剩余域$k$的混合特征完备离散赋值域.设$X$是$k$上的簇，$Y$是$X$的开，$Y'$是$Y$在$X$中稠密的开.我们扩展Kedlaya的完全忠实如下（我们不假设$Y$顺利）：规范函子$F\text{-}\mathrm{Isoc} ^† (Y,X/K) \to F\text{-}\mathrm{Isoc} ^† (Y,Y/K) $是完全忠实。假设现在$Y$是光滑的。我们构造了$(Y,X)$上的部分过相干等晶范畴，记为$\mathrm{Isoc} ^{††} (Y,X/K) $，其对象是某些特殊的算术$\D$ -模.此外，我们检查范畴$\sp_{(Y,X),+} : \mathrm{Isoc} ^† (Y,X/K) \cong \mathrm{Isoc} ^{††} (Y,X/K)$的等价性。
英文摘要：
Let $K$ be a mixed characteristic complete discrete valuation field with perfect residue field $k$. Let $X$ be a variety over $k$, $Y$ be an open of $X$, $Y'$ be an open of $Y$ dense in $X$. We extend Kedlaya's full faithfulness as follows (we do not suppose $Y$ to be smooth): the canonical functor $F\text{-}\mathrm{Isoc} ^† (Y,X/K) \to F\text{-}\mathrm{Isoc} ^† (Y,Y/K) $ is fully faithfull. Suppose now $Y$ smooth. We construct the category of partially overcoherent isocrystals over $(Y,X)$ denoted by $\mathrm{Isoc} ^{††} (Y,X/K) $ whose objects are some particular arithmetic $\D$-modules. Furthermore, we check the equivalence of categories $\sp_{(Y,X),+} : \mathrm{Isoc} ^† (Y,X/K) \cong \mathrm{Isoc} ^{††} (Y,X/K)$.
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