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You searched for +publisher:"University of Illinois – Chicago" +contributor:("Gillet, Henri"). Showing records 1 – 2 of 2 total matches.

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University of Illinois – Chicago

1. Berner, Joseph. Shape Theory in Homotopy Theory and Algebraic Geometry.

Degree: 2018, University of Illinois – Chicago

This work defines the étale homotopy type in the context of non-archimedean geometry, in both Berkovich’s and Huber’s formalisms. To do this we take the shape of a site’s associated hypercomplete 1-topos. This naturally leads to discussing localizations of the category of pro-spaces. For a prime number p, we introduce a new localization intermediate between profinite spaces and {p}`-profinite spaces. This new category is well suited for comparison theorems when working over a discrete valuation ring of mixed characteristic. We prove a new comparison theorem on the level of topoi for the formalisms of Berkovich and Huber, and prove an analog of smooth-proper base change for nonarchimedean analytic spaces. This provides a necessary result for the non-archimedean analog of Friedlander’s homotopy fiber theorem, which we prove. For a variety over a non-archimedean field, we prove a comparison theorem between the classical étale homotopy type and our étale homotopy type of the variety’s analytification. Finally, we examine certain log formal schemes over the formal spectrum of a complete discrete valuation ring, and compare their Kummer étale homotopy type with the étale homotopy type of the associated non-archimedean analytic space. Advisors/Committee Members: Gillet, Henri (advisor), Shipley, Brooke (committee member), Antieau, Ben (committee member), Lesieutre, John (committee member), Gepner, David (committee member), Gillet, Henri (chair).

Subjects/Keywords: Homotopy Theory; Algebraic Geometry; Higher Category Theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Berner, J. (2018). Shape Theory in Homotopy Theory and Algebraic Geometry. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23085

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Berner, Joseph. “Shape Theory in Homotopy Theory and Algebraic Geometry.” 2018. Thesis, University of Illinois – Chicago. Accessed June 07, 2020. http://hdl.handle.net/10027/23085.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Berner, Joseph. “Shape Theory in Homotopy Theory and Algebraic Geometry.” 2018. Web. 07 Jun 2020.

Vancouver:

Berner J. Shape Theory in Homotopy Theory and Algebraic Geometry. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2020 Jun 07]. Available from: http://hdl.handle.net/10027/23085.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Berner J. Shape Theory in Homotopy Theory and Algebraic Geometry. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/23085

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of Illinois – Chicago

2. Bayindir, Haldun Ozgur. Topological Equivalences of E-infinity Differential Graded Algebras.

Degree: 2018, University of Illinois – Chicago

Two DGAs are said to be topologically equivalent when the corresponding Eilenberg–Mac Lane ring spectra are weakly equivalent as ring spectra. Quasi-isomorphic DGAs are topologically equivalent, but the converse is not necessarily true. As a counterexample, Dugger and Shipley showed that there are DGAs that are nontrivially topologically equivalent, ie topologically equivalent but not quasi-isomorphic. In this work, we define E-infinity topological equivalences and utilize the obstruction theories developed by Goerss, Hopkins and Miller to construct first examples of nontrivially E-infinity topologically equivalent E-infinity DGAs. Also, we show using these obstruction theories that for coconnective E-infinity Fp–DGAs, E-infinity topological equivalences and quasi-isomorphisms agree. For E-infinity Fp–DGAs with trivial first homology, we show that an E-infinity topological equivalence induces an isomorphism in homology that preserves the Dyer–Lashof operations and therefore induces an H-infinity Fp–equivalence. Advisors/Committee Members: Shipley, Brooke (advisor), Bousfield, Aldridge K (committee member), Antieau, Benjamin (committee member), Gillet, Henri (committee member), Mathew, Akhil (committee member), Shipley, Brooke (chair).

Subjects/Keywords: Dyer-Lashof operations; Differential graded algebras; Commutative ring spectra; Obstruction theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Bayindir, H. O. (2018). Topological Equivalences of E-infinity Differential Graded Algebras. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/23145

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Thesis, University of Illinois – Chicago. Accessed June 07, 2020. http://hdl.handle.net/10027/23145.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Bayindir, Haldun Ozgur. “Topological Equivalences of E-infinity Differential Graded Algebras.” 2018. Web. 07 Jun 2020.

Vancouver:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2020 Jun 07]. Available from: http://hdl.handle.net/10027/23145.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bayindir HO. Topological Equivalences of E-infinity Differential Graded Algebras. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/23145

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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