论文标题
本地Noetherian方案的刚性刚性同谋第2部分：晶体
Rigid cohomology of locally noetherian schemes Part 2 : Crystals
论文作者
论文摘要
我们介绍了过度会议位点的一般概念和在过度会议的位置上的可构造晶体。我们表明，如果$ v $是本地noepherian正式方案$ x $ x $ x $ x $ x $ y y $ \ mathbb q $上的几何实现，那么$ x/o $上的可构造晶体的类别等效于构造模块的类别，这些模块与the the the the the the the the the the the the the the the the the the the the the the the tube $ \，x $ \ x $ x $ x $ x $ x $ x $ x $ n $我们还表明，可构造晶体的共同体学与其在管$ \，] x [_v $上实现的de rham共同体同构是同构。这是对刚性的同胞学的概括。最后，我们证明了相对于$ h $ - 血统相对于可构造晶体的普遍共同下降和普遍有效下降。这包含平坦，适当的下降，并概括了所有先前的下降导致僵化的同胞学。
We introduce the general notions of an overconvergent site and a constructible crystal on an overconvergent site. We show that if $V$ is a geometric materialization of a locally noetherian formal scheme $X$ over an analytic space $O$ defined over $\mathbb Q$, then the category of constructible crystals on $X/O$ is equivalent to the category of constructible modules endowed with an overconvergent connection on the tube $\,]X[_V$ of $X$ in $V$. We also show that the cohomology of a constructible crystal is then isomorphic to the de Rham cohomology of its realization on the tube $\,]X[_V$. This is a generalization of rigid cohomology. Finally, we prove universal cohomological descent and universal effective descent with respect to constructible crystals with respect to the $h$-topology. This encompass flat and proper descent and generalizes all previous descent results in rigid cohomology.
