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

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2019-09-23

Authors

Reyes, Nicolas Z.

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Abstract

The 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.

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