Lectures on Etale Cohomology
نویسنده
چکیده
These are the notes for a course taught at the University of Michigan in W89 as Math 732 and in W98 as Math 776. They are available at www.math.lsa.umich.edu/∼jmilne/ Please send comments and corrections to me at [email protected]. v2.01 (August 9, 1998). First version on the web.
منابع مشابه
Etale Cohomology of Rigid Analytic Spaces
The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...
متن کاملPRO-ÉTALE COHOMOLOGY Contents
Contents 1. Introduction 1 2. Some topology 2 3. Local isomorphisms 4 4. Ind-Zariski algebra 6 5. Constructing w-local affine schemes 6 6. Identifying local rings versus ind-Zariski 10 7. Ind-´ etale algebra 14 8. Constructing ind-´ etale algebras 15 9. Weaklyétale versus pro-´ etale 18 10. Constructing w-contractible covers 18 11. The pro-´ etale site 21 12. Points of the pro-´ etale site 29 1...
متن کاملEtale Homotopy and Sums-of-squares Formulas
This paper uses a relative of BP -cohomology to prove a theorem in characteristic p algebra. Speci cally, we obtain some new necessary conditions for the existence of sums-of-squares formulas over elds of characteristic p > 2. These conditions were previously known in characteristic zero by results of Davis. Our proof uses a generalized etale cohomology theory called etale BP2.
متن کاملPro-´ Etale Cohomology
0965 Contents 1. Introduction 1 2. Some topology 2 3. Local isomorphisms 4 4. Ind-Zariski algebra 6 5. Constructing w-local affine schemes 6 6. Identifying local rings versus ind-Zariski 10 7. Ind-´ etale algebra 14 8. Constructing ind-´ etale algebras 15 9. Weaklyétale versus pro-´ etale 18 10. Constructing w-contractible covers 18 11. The pro-´ etale site 21 12. Points of the pro-´ etale site...
متن کامل