pdf file for the current version (2.21)
These are the notes for a course taught at the University of
Michigan in 1989 and 1998. In comparison with my book, the
emphasis is on heuristic arguments rather than formal proofs
and on varieties rather than schemes. The notes also discuss
the proof of the Weil conjectures (Grothendieck and
- Etale Morphisms
- The Etale Fundamental Group
- The Local Ring for the Etale Topology
- Sheaves for the Etale Topology
- The Category of Sheaves on Xet.
- Direct and Inverse Images of Sheaves.
- Cohomology: Definition and the Basic Properties
- Cech Cohomology
- Principal Homogeneous Spaces and H1.
- Higher Direct Images; the Leray Spectral Sequence
- The Weil-Divisor Exact Sequence and the Cohomology of Gm
- The Cohomology of Curves
- Cohomological Dimension.
- Purity; the Gysin Sequence.
- The Proper Base Change Theorem.
- Cohomology Groups with Compact Support.
- Finiteness Theorems; Sheaves of Zl-modules
- The Smooth Base Change Theorem.
- The Comparison Theorem.
- The Kunneth Formula.
- The Cycle Map; Chern Classes
- Poincare Duality
- Lefschetz Fixed-Point Formula.
- The Weil Conjectures.
- Proof of the Weil Conjectures, except for the Riemann
- Preliminary Reductions
- The Lefschetz Fixed Point Formula for Nonconstant Sheaves
- The MAIN Lemma
- The Geometry of Lefschetz Pencils
- The Cohomology of Lefschetz Pencils
- Completion of the Proof of the Weil Conjectures.
- The Geometry of Estimates
v2.01; August 9, 1998; first version on the web; 190 pages.
v2.10; May 20, 2008; corrected errors and improved the TeX; 196 pages.
old version 2.10
v2.20; May 3, 2012; corrected; minor improvements; 202 pages.
v2.21; March 22, 2013; corrected; minor improvements; 202 pages.