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Type: Thesis
Title: Higher Tannaka duality.
Author: Wallbridge, James
Issue Date: 2011
School/Discipline: School of Mathematical Sciences
Abstract: In this thesis we prove a Tannaka duality theorem for (∞, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (∞, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toёn. We also describe three applications of our theory: perfect complexes and that of both motives and its non-commutative analogue due to Kontsevich.
Advisor: Varghese, Mathai
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2011
Keywords: Tannaka duality; (∞, 1) - category; stack; gerbe; derived algebraic geometry
Appears in Collections:Research Theses

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