上同调组构：与严格上同调的留置权
Cohomologie syntomique: liens avec les cohomologies étale et rigide
摘要：
本文定义的联上同调将刚性上同调与标准上同调联系起来，将后者看作前者在Frobenius下的不动点.设V是一个完备的离散赋值环，具有特征p > 0的完美剩余域k = V/m和特征0的分式域K.在定义了k-概型X上交换层G的具有紧支撑的同分上同调后，证明了当G是lisse层时，它与具有紧支撑的etale上同调是一致的.若G的收敛F-同晶来自于过收敛同晶E，则E的刚性上同调表示为同分上同调的极限：G的紧支集上同调是Frobenius作用于E的刚性上同调的不动点.
英文摘要：
Syntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E.
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