Riemann-Hilbert correspondence for unit $F$-crystals on embeddable algebraic varieties
Riemann-Hilbert correspondence for unit $F$-crystals on embeddable algebraic varieties
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可嵌入代数簇上单位$F$晶体的黎曼-希尔伯特对应关系
DOI：
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发表时间：
2016
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通讯作者：
Sachio Ohkawa
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作者：
Sachio Ohkawa
对于特征p>0的理想域k上的有限型分离格式X，当它浸入截断Witt环W_{n}上的真光滑格式时，我们定义了在W_{n}上X上的具有有限Tor维数的局部非线性生成的单位F-晶体的有界导出范畴，而与浸入的选择无关.然后证明了该范畴与有限Tor维数${mathbb Z}/{p^{n}{mathbb Z}}$-模的可构造余层的有界导范畴的反等价性.我们还讨论了当n=1时，这些导范畴上的t-结构之间的关系.我们的结果是一个推广的黎曼希尔伯特对应单位$F$-晶体由于Emerton-Kisin的情况下（可能是奇异的）嵌入代数簇的特征$p>0$。
For a separated scheme $X$ of finite type over a perfect field $k$ of characteristic $p>0$ which admits an immersion into a proper smooth scheme over the truncated Witt ring $W_{n}$, we define the bounded derived category of locally finitely generated unit $F$-crystals with finite Tor-dimension on $X$ over $W_{n}$, independently of the choice of the immersion. Then we prove the anti-equivalence of this category with the bounded derived category of constructible 'etale sheaves of ${mathbb Z}/{p^{n}{mathbb Z}}$-modules with finite Tor dimension. We also discuss the relationship of $t$-structures on these derived categories when $n=1$. Our result is a generalization of the Riemann-Hilbert correspondence for unit $F$-crystals due to Emerton-Kisin to the case of (possibly singular) embeddable algebraic varieties in characteristic $p>0$.