Higher Tannaka duality.
Date
2011
Authors
Wallbridge, James
Editors
Advisors
Varghese, Mathai
Journal Title
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Type:
Thesis
Citation
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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.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2011