RECONSTRUCTION OFDELIGNE CLASSES AND COCYCLESDissertationzur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.)in der Wissenschaftsdisziplin Mathematik/Geometrieeingereicht an derMathematisch-Naturwissenschaftlichen Fakultat¨der Universitat¨ Potsdamvon Aydın Demircioglu˘Institut fur¨ Mathematik, Universitat¨ PotsdamAlbert-Einstein Institut, Potsdam This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.The day will surely come when you see the true believers,men and women, with their lights shining before them and ontheir right hands, and a voice saying to them: ’Rejoice this day.You shall enter gardens watered by flowing streams. in whichyou shall abide for ever.’ This is the supreme triumph.On that day, the hypocrites, men and women, will say to thetrue believers: ’Wait for us, that we may borrow some of yourlight.’ But they will be told: ’Go back, and seek some otherlight!’A wall with a gate shall be set before them. Inside there shall bemercy, and without, to the fore, the scourge of Hell. They willcall out to them, saying: ’Were we not on your side?’ ’Yes,’they will reply, ’but you tempted yourselves, you wavered, youdoubted, and were deceived by vain desires, until His judge-ment came. You were diverted from Him by illusions. The Fireshall be your home: you have justly earned it, an evil end!’.