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On Picard 2-Stacks and Length 3 Complexes of Abelian Sheaves

Title: On Picard 2-Stacks and Length 3 Complexes of Abelian Sheaves.
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Name(s): Tatar, Ahmet Emin, 1979-, author
Aldrovandi, Ettore, professor directing thesis
Capstick, Simon, university representative
Agashe, Amod, committee member
Aluffi, Paolo, committee member
Klassen, Eric, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2010
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: In Seminaire de Geometrie Algebrique 4 (SGA4), Expose XVIII, Pierre Deligne proves that to any Picard stack one can associate a complex of abelian sheaves of length 2. He also studies the morphisms between such stacks and shows that such a morphism defines a class of fractions in the derived category of complexes of abelian sheaves of length 2. From these two preliminary results, he finally deduces that the derived category of complexes of abelian sheaves of length 2 is equivalent to the category of Picard stacks with morphisms being the isomorphism classes. In this dissertation, we generalize his work, following closely his steps in SGA4, to the case of Picard 2-stacks. But this generalization requires first a clear description of a Picard 2-category as well as of a 2-functor between such 2-categories that respects Picard structure. Once this has been done, we can talk about category of Picard 2-stacks and prove that the derived category of complexes of abelian sheaves of length 3 is equivalent to the category of Picard 2-stacks.
Identifier: FSU_migr_etd-1674 (IID)
Submitted Note: A Thesis submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2010.
Date of Defense: May 24, 2010.
Keywords: 2-Categories, Torsors, Complexes, 3-Categories, Picard Stacks, Abelian Sheaves
Bibliography Note: Includes bibliographical references.
Advisory Committee: Ettore Aldrovandi, Professor Directing Thesis; Simon Capstick, University Representative; Amod Agashe, Committee Member; Paolo Aluffi, Committee Member; Eric Klassen, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-1674
Owner Institution: FSU

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Tatar, A. E. (2010). On Picard 2-Stacks and Length 3 Complexes of Abelian Sheaves. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-1674