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Title: On the Serre-Swan theorem, and on vector bundles over real Abelian varieties
Researcher: Morye, Archana Subhash
Guide(s): Raghavendra, N
Keywords: Serre-Swan theorem
vector bundles
Abelian varieties
Upload Date: 13-Sep-2012
University: Homi Bhabha National Institute
Completed Date: March, 2011
Abstract: This thesis is divided into two parts. In Chapter 1 we prove a generalization of two classical results of Serre and Swan on the relation between locally free sheaves and projective modules, by emphasizing the axiomatic aspect of the problem. We determine a class of ringed spaces (X,OX) for which the category of locally free sheaves of bounded rank over X is equivalent to the category of finitely generated projective _(X,OX) modules. The well-known Serre-Swan theorems for affine schemes, differentiable manifolds, Stein spaces, etc., are then derived. In Chapter 2 we study real algebraic vector bundles over a real abelian variety. The main theorem in this part gives various equivalent criteria for a real algebraic vector bundle over a real abelian variety to admit a flat holomorphic connection. In the course of the proof of the main theorem we also derive a version of a result of Simpson for real abelian varieties.
Pagination: 102p.
Appears in Departments:Department of Mathematical Sciences

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01_title.pdfAttached File61.58 kBAdobe PDFView/Open
02_certificate.pdf22.69 kBAdobe PDFView/Open
03_declaration.pdf23.3 kBAdobe PDFView/Open
04_acknowledgements.pdf28.38 kBAdobe PDFView/Open
05_abstract.pdf50.51 kBAdobe PDFView/Open
06_synopsis.pdf138.37 kBAdobe PDFView/Open
07_dedication.pdf13.09 kBAdobe PDFView/Open
08_contents.pdf71.55 kBAdobe PDFView/Open
09_conventions and notations.pdf77.82 kBAdobe PDFView/Open
10_chapter 1.pdf97.34 kBAdobe PDFView/Open
11_chapter 2.pdf360.24 kBAdobe PDFView/Open
12_chapter 3.pdf332.5 kBAdobe PDFView/Open
13_appendix.pdf116.59 kBAdobe PDFView/Open
14_bibliography.pdf64.24 kBAdobe PDFView/Open
15_index.pdf105.28 kBAdobe PDFView/Open

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