Indian Institute of Technology, Bombay,

Powai, Mumbai 400076, India

Institut de Mathématiques de Luminy

Luminy Case 907, 13288 Marseille, Cedex 9, France

Introduction | 2 | |

1 | Singular Loci and Regular Flags | 4 |

2 | Weak Lefschetz Theorem for Singular Varieties | 6 |

3 | Cohomology of Complete Intersections | 10 |

4 | The Central Betti Number of Complete Intersections | 12 |

5 | Zeta Functions and the Trace Formula | 14 |

6 | Number of Points of Complete Intersections | 16 |

7 | Complete Intersections with isolated singularities | 18 |

8 | The Penultimate Betti Number | 21 |

9 | Cohomology and Albanese Varieties | 24 |

10 | A Conjecture of Lang and Weil | 28 |

11 | On the Lang-Weil Inequality | 32 |

12 | Number of Points of Algebraic Sets | 35 |

References | 36 |

This paper is published in:

Preliminary versions of this paper have appeared in preprint form as Prétirage No. 99-13 (April 1999) and Prétirage No. 2001-32 (July 2001) of the Institut de Mathématiques de Luminy, Marseille, France.

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