Sums of Betti Numbers in Arbitrary Characteristic
By Nicholas M. Katz. 2001
96 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3ce5f8ec540ac3abfb1df8410b1bd868c993a6b4
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- \'Etale cohomology, Lefschetz Theorems and Number of Points of Singular Varieties over Finite Fields (2008, methodology): “The explicit formula (2) is a consequence of the work of Hirzebruch [17] and Jouanolou [20] on nonsingular complete intersections, while the computable bound (4) is obtained using some work of Katz [24] on the sums of Betti numbers.”
- Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil (2002, result): “There are now shorter proofs of the Riemann hypothesis for varieties over finite fields: by Laumon in 1984 and most recently by Katz [20].”