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AuthorTamme, Gรผter. author
TitleIntroduction to ร{137}tale Cohomology [electronic resource] / by Gรผter Tamme
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994
Edition 1
Connect tohttp://dx.doi.org/10.1007/978-3-642-78421-7
Descript IX, 186 p. online resource

SUMMARY

ร{137}tale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory. It has, in the last decades, brought fundamental new insights in arithmetic and algebraic geometric problems with many applications and many important results. The book gives a short and easy introduction into the world of Abelian Categories, Derived Functors, Grothendieck Topologies, Sheaves, General ร{137}tale Cohomology, and ร{137}tale Cohomology of Curves


CONTENT

0. Preliminaries -- ยง1. Abelian Categories -- ยง2. Homological Algebra in Abelian Categories -- ยง3. Inductive Limits -- I. Topologies and Sheaves -- ยง1. Topologies -- ยง2. Abelian Presheaves on Topologies -- ยง3. Abelian,Sheaves on Topologies -- II. ร{137}tale Cohomology -- ยง1. The ร{137}tale Site of a Scheme -- ยง2. The Case X= spec(k) -- ยง3. Examples of ร{137}tale Sheaves -- ยง4. The Theories of Artin-Schreier and of Kummer -- ยง5. Stalks of ร{137}tale Sheaves -- ยง6. Strict Localizations -- ยง7. The Artin Spectral Sequence -- ยง8. The Decomposition Theorem. Relative Cohomology -- ยง9. Torsion Sheaves, Locally Constant Sheaves, Constructible Sheaves -- ยง10. ร{137}tale Cohomology of Curves -- ยง11. General Theorems in ร{137}tale Cohomology Theory


Mathematics Algebraic geometry K-theory Number theory Algebraic topology Mathematics Algebraic Geometry Algebraic Topology K-Theory Number Theory



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