The moduli space of objects in differential graded categories glued along bimodules and a presentability result in the homotopy theory of commutative differential graded algebras

dc.contributor.advisorBlumberg, Andrew J.
dc.contributor.committeeMemberBen-Zvi, David
dc.contributor.committeeMemberKeel, Sean
dc.contributor.committeeMemberGepner, David
dc.creatorReyes, Nicolas Z.
dc.creator.orcid0000-0001-5183-3211
dc.date.accessioned2019-12-11T21:10:39Z
dc.date.available2019-12-11T21:10:39Z
dc.date.created2019-08
dc.date.issued2019-09-23
dc.date.submittedAugust 2019
dc.date.updated2019-12-11T21:10:40Z
dc.description.abstractThe moduli space of objects of a dg-category, T, is a derived stack introduced in (31) that paramatrizes "pseudo-perfect T [superscript op] -modules." This construction extends to a Morita invariant functor, [mathematical forumla], which is right adjoint to the functor that assigns to a derived stack it's dg-category of perfect complexes. In this thesis we are primarily concerned with the behavior of semi-orthogonal decompositions of dg categories under this functor. We show that when a dg category, C has a semi-orthogonal decomposition, H⁰ (C) =< H⁰(C₀), H⁰ (C₁) >, the moduli space of objects in C can be expressed as a certain pullback of stacks involving the moduli spaces of objects in C₀ and C₁. We also present a result on the cofibrant generation of a certain model category obtained as the total space of the Grothendieck fibration associated to the "module category" functor mapping a derived ring to its model category of modules.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/78717
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/5773
dc.language.isoen
dc.subjectHomotopy theory
dc.titleThe moduli space of objects in differential graded categories glued along bimodules and a presentability result in the homotopy theory of commutative differential graded algebras
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
REYES-DISSERTATION-2019.pdf
Size:
359.93 KB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.45 KB
Format:
Plain Text
Description:
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.84 KB
Format:
Plain Text
Description: