Lectures on Algebraic Geometry II

Basic Concepts, Coherent Cohomology, Curves and their Jacobians
2011
ISBN: 978-3-8348-0432-7
Verlag: Vieweg+Teubner Verlag

Buch, Englisch, Band 39, 365 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 890 g

Reihe: Aspects of Mathematics

This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved.
Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

Zielgruppe

Mathematiker und Studierende höherer Semester, die sich für algebraische Geometrie und deren Beziehungen zur Topologie und zur Zahlentheorie in der Forschung interessieren

Autoren/Hrsg.

Harder, Günter

Weitere Mitwirkende

Diederich, Klas

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Basic concepts of the Theory of Schemes - Some Commutative Algebra - Projective Schemes - Curves and the Theorem of Riemann-Roch - The Picard functor for curves and Jacobians

Über Autor(innen)

Harder, Günter
Prof. Dr. Günter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany.

Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn