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You searched for +publisher:"University of Illinois – Chicago" +contributor:("Antieau, Ben"). One record found.

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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

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