In the first part of this thesis we give some comparison results about Dg-categories, A∞-categories and stable ∞-categories. In the second part we introduce the theory of noncommutative motives and we solve the Voevodsky nilpotence conjecture for cubic 4folds and some GM-4folds.
COMPARISON RESULTS ABOUT DG-CATEGORIES, A∞-CATEGORIES, STABLE ∞-CATEGORIES AND NONCOMMUTATIVE MOTIVES / M. Ornaghi ; tutor: P. Stellari ; coordinatore: V. Mastropietro. - : . DIPARTIMENTO DI MATEMATICA "FEDERIGO ENRIQUES", 2018 Mar 15. ((30. ciclo, Anno Accademico 2017. [10.13130/ornaghi-mattia_phd2018-03-15].
COMPARISON RESULTS ABOUT DG-CATEGORIES, A∞-CATEGORIES, STABLE ∞-CATEGORIES AND NONCOMMUTATIVE MOTIVES
M. Ornaghi
2018
Abstract
In the first part of this thesis we give some comparison results about Dg-categories, A∞-categories and stable ∞-categories. In the second part we introduce the theory of noncommutative motives and we solve the Voevodsky nilpotence conjecture for cubic 4folds and some GM-4folds.
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