Number of Points of Singular Varieties over Finite Fields
Corrigenda and Addenda:
Étale Cohomology, Lefschetz Theorems and
Number of Points of Singular Varieties over Finite Fields1
Sudhir R. Ghorpade
Department of Mathematics
Indian Institute of Technology, Bombay,
Powai, Mumbai 400076, India E-Mail: srg@math.iitb.ac.in
and
Gilles Lachaud
Équipe ``Arithmétique
et Théorie de l'Information''
Institut de Mathématiques de Luminy
Luminy Case 907, 13288 Marseille, Cedex 9, France E-Mail: lachaud@iml.univ-mrs.fr
Abstract
Brian Conrad had pointed out to us that the proof of Proposition 9.8 in our
MMJ article
is incomplete. In this supplement,
we provide the missing arguments together with a few other corrections.
We also use the opportunity to indicate some new consequences of our results,
and mention some applications of the results in the
MMJ article
Contents
Base Field
1
Betti Numbers of Curves
2
The Penultimate Cohomology Group
4
Addenda
6
Additions and Compements
7
Supplementary References
7
1
2000 Mathematics Subject Classification.
11G25, 14F20, 14G15, 14M10.
This paper is published in:
Moscow Mathematical Journal, Vol. 9, No. 2 (2009), pp. 431--438.
A revised version of the
MMJ article
taking into account the corrections and additions in this supplement
is available on the arXiv.org.