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- W2963706468 abstract "Let V⊂Pn(F‾q) be a complete intersection defined over a finite field Fq of dimension r and singular locus of dimension at most 0≤s≤r−2. We obtain an explicit version of the Hooley–Katz estimate ||V(Fq)|−pr|=O(q(r+s+1)/2), where |V(Fq)| denotes the number of Fq-rational points of V and pr:=|Pr(Fq)|. Our estimate improves all the previous estimates in several important cases. Our approach relies on tools of classical algebraic geometry. A crucial ingredient is a new effective version of the Bertini smoothness theorem, namely an explicit upper bound of the degree of a proper Zariski closed subset of (Pn)s+1(F‾q) which contains all the singular linear sections of V of codimension s+1." @default.
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- W2963706468 date "2016-01-01" @default.
- W2963706468 modified "2023-09-23" @default.
- W2963706468 title "Explicit estimates for the number of rational points of singular complete intersections over a finite field" @default.
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- W2963706468 doi "https://doi.org/10.1016/j.jnt.2015.06.007" @default.
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