Buch, Englisch, Band 1708, 135 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 240 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1708, 135 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 240 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-66312-6
Verlag: Springer Berlin Heidelberg
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Topologie Algebraische Topologie
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
Introduction.- Preliminaries.- Review of Algebraic groups over arbitrary fields.- Representations of phi1 and the Moduli space.- p-adic norm on a vector space and Bruhat-Tits buildings.- Harmonic metric on flat vector bundle.- Pluriharmonic map of finite energy.- Pluriharmonic maps of possibly infinite energy but with controlled growth at infinity.- Non-abelian Hodge theory, factorization theorems for non rigid or p-adic unbound representations.- Higgs bundles for archimedean representations and equivariant holomorphic 1-forms for p-adic representations.- Albanese maps and a Lefschetz type theorem for holomorphic 1-forms.- Factorizations for nonrigid representations into almost simple complex algebraic groups.- Factorization for p-adic unbounded representations into almost simple p-adic algebraic groups.- Simpson's construction of families on non rigid representations.- Shavarevich maps for representations of phi1, Kodaira dimension and Chern-hyperbolicity of Shavarevich varieties.
