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TY - CHAP
TI - Introduction.
A2 - Berthelot, Pierre
A2 - Ogus, Arthur
AB - Let k be the field with q elements, X/k a smooth, projective, and geometrically connected scheme. One wants to know how many rational points X has, or more generally, the number c_{ν}of k_{ν}-valued points of X where k_{ν}is the extension of k of degree ν. The values of these numbers are conveniently summarized in the zeta function of X, given by${{\text{Z}}_{\text{X}}}(\text{t})=\exp \sum\limits_{\nu =1}^{\infty }{\frac{{{\text{c}}_{\nu }}}{\nu }{{\text{t}}^{\nu }}}$. This can also be written as$\underset{\text{x}}{\mathop{\prod }}\,\frac{1}{[1-{{\text{t}}^{\deg \text{x}}}]}$, the product being taken over the closed points x of X, where deg x means the degree of the residue field k(x) over k. It is clear

EP - 1.14
PB - Princeton University Press
PY - 1978
SN - null
SP - 1.1
T2 - Notes on Crystalline Cohomology. (MN-21)
UR - http://www.jstor.org/stable/j.ctt130hk6f.4
Y2 - 2021/09/21/
ER -