On Witt vector cohomology for singular varieties
On Witt vector cohomology for singular varieties
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DOI：
10.1112/s0010437x06002533
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发表时间：
2007-03-01
影响因子：
1.8
通讯作者：
Esnault, Helene
中科院分区：
文献类型：
--
作者：
Berthelot, Pierre;Bloch, Spencer;Esnault, Helene
在特征p > 0的理想域k上，我们构造了有限型分离k-格式的“紧支撑Witt向量上同调”，推广了（用Q张量化后）真k-格式的经典理论.我们定义了一个从紧支集刚性上同调到紧支集Witt向量上同调的典范态射，并证明了它提供了后者与前者的斜率< 1部分之间的一个恒等式.在一个有限域上，这允许我们在特殊的例子中计算有理点个数的同余。特别是，同余模基数的有限域的数量的合理点的theta因子的阿贝尔品种不依赖于选择的theta因子。这肯定地回答了J. P. Serre。
Over a perfect field k of characteristic p > 0, we construct a 'Witt vector cohomology with compact supports' for separated k-schemes of finite type, extending (after tensorization with Q) the classical theory for proper k-schemes. We define a canonical morphism from rigid cohomology with compact supports to Witt vector cohomology with compact supports, and we prove that it provides an identification between the latter and the slope < 1 part of the former. Over a finite field, this allows one to compute congruences for the number of rational points in special examples. In particular, the congruence modulo the cardinality of the finite field of the number of rational points of a theta divisor on an abelian variety does not depend on the choice of the theta divisor. This answers positively a question by J.-P. Serre.