Kobayashi-Hitchin correspondence for tame harmonic bundles and an application

The Author Establishes The Correspondence Between Tame Harmonic Bundles And $\mu --l$-polystable Parabolic Higgs Bundles With Trivial Characteristic Numbers. He Also Shows The Bogomolov-gieseker Type Inequality For $\mu --l$-stable Parabolic Higgs Bundles. The Author Shows That Any Local System On A Smooth Quasiprojective Variety Can Be Deformed To A Variation Of Polarized Hodge Structure. He Then Concludes That Some Kind Of Discrete Groups Cannot Be A Split Quotient Of The Fundamental Group Of A Smooth Quasiprojective Variety. 1. Introduction -- 2. Preliminary -- 3. Parabolic Higgs Bundle And Regular Filtered Higgs Bundle -- 4. An Ordinary Metric For A Parabolic Higgs Bundle -- 5. Parabolic Higgs Bundle Associated To Tame Harmonic Bundle -- 6. Preliminary Correspondence And Bogomolov-gieseker Inequality -- 7. Construction Of A Frame -- 8. Some Convergence Results -- 9. Existence Of Adapted Pluri-harmonic Metric -- 10. Torus Action And The Deformation Of Representations --- G-harmonic Bundle. Takuro Mochizuki. Includes Bibliographical References (p. [113]-117). Abstract Also In French.