Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/69436
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 |
Files in This Item:
File | Description | Size | Format | |
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01front.pdf | 139.14 kB | Adobe PDF | View/Open | |
02whole.pdf | 760.24 kB | Adobe PDF | View/Open |
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