Introduction to Étale Cohomology
Springer Berlin (Verlag)
978-3-540-57116-2 (ISBN)
Étale 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 Étale Cohomology, and Étale Cohomology of Curves.
Étale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory. It is a large area with a large number of applications. The book gives a quick and easy introduction into Étale Cohomology. It is ample in its arguments but wisely restricted in the choice of material.
0. Preliminaries.-
1. Abelian Categories.-
2. Homological Algebra in Abelian Categories.-
3. Inductive Limits.- I. Topologies and Sheaves.-
1. Topologies.-
2. Abelian Presheaves on Topologies.-
3. Abelian,Sheaves on Topologies.- II. Étale Cohomology.-
1. The Étale Site of a Scheme.-
2. The Case X= spec(k).-
3. Examples of Étale Sheaves.-
4. The Theories of Artin-Schreier and of Kummer.-
5. Stalks of Étale Sheaves.-
6. Strict Localizations.-
7. The Artin Spectral Sequence.-
8. The Decomposition Theorem. Relative Cohomology.-
9. Torsion Sheaves, Locally Constant Sheaves, Constructible Sheaves.-
10. Étale Cohomology of Curves.-
11. General Theorems in Étale Cohomology Theory.
| Erscheint lt. Verlag | 28.9.1994 |
|---|---|
| Reihe/Serie | Universitext |
| Übersetzer | M. Kolster |
| Zusatzinfo | IX, 186 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 310 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Abelian varieties • Abelsche Varietäten • cohomology • Cohomology theory • derived functors • Derivierte Funktoren • Etale cohomology • etale Kohomologie • Garben • grothendieck • Grothendieck Topology • Homological algebra • Homology • Kohomologie • Number Theory • Sheaves • Topologien |
| ISBN-10 | 3-540-57116-7 / 3540571167 |
| ISBN-13 | 978-3-540-57116-2 / 9783540571162 |
| Zustand | Neuware |
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