Etale Cohomology of Rigid Analytic Spaces
نویسندگان
چکیده
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 rigid cohomology are re-established. Key Phrases: " etale cohomology", "rigid analytic spaces", "rigid cohomology", "overconvergent sheaves" 1991 Mathematics Subject Classi cation: Primary 26E30, secondary 14F20.
منابع مشابه
Navigating the motivic world
Contents Introduction 1 Chapter 1. Introduction to the Weil conjectures 3 1. A first look 3 2. Formal statement of the conjectures 8 3. Zeta functions 11 4. A plan to prove the conjectures 14 5. Some history of the proofs of the conjectures 18 A. Computer calculations 20 B. Computations for diagonal hypersurfaces 25 Chapter 2. Topological interlude: the cohomology of algebraic varieties 35 1. L...
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 کاملEtale Cohomology
The development of etale cohomology was motivated by work on the Weil conjectures, which state that local-zeta functions ζ(X, s), i.e. the generating function for the number of rational points of a projective variety defined over a finite field Fq in all finite extensions, satisfy certain properties analogous to those of the Riemann zeta function. Weil observed that the number of points defined...
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 کامل