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Topics in Algebraic K-theory

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dc.contributor.advisor HOGADI, AMIT en_US
dc.contributor.author K, ARUN KUMAR en_US
dc.date.accessioned 2016-05-06T10:47:34Z
dc.date.available 2016-05-06T10:47:34Z
dc.date.issued 2016-05 en_US
dc.identifier.uri http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/631
dc.description.abstract The objective of this thesis is to study the algebraic K-theory of exact categories. In algebraic K-theory we construct a sequence of groups, called K n , which are invari- ants of a given exact category. We look at two different constructions of K n , Quillen’s Q-construction of the K-groups of an exact category as the homotopy groups of a topological space and Wladhausen’s S-construction of the K-groups as the stable ho- motopy groups of a spectrum, and show that they are equivalent. The S-construction is then used to prove the main aim of this thesis, the additivity theorem. The ad- ditivity theorem then helps us prove fundamental results about the K-groups. The main results considered are, the cofinality theorem and resolution theorem for exact categories, and the devissage theorem and localisation theorem for abelian categories. en_US
dc.language.iso en en_US
dc.subject 2016
dc.subject Algebraic K-theory en_US
dc.subject Algebraic geometry en_US
dc.title Topics in Algebraic K-theory en_US
dc.type Thesis en_US
dc.type.degree BS-MS en_US
dc.contributor.department Dept. of Mathematics en_US
dc.contributor.registration 20111023 en_US


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  • MS THESES [1705]
    Thesis submitted to IISER Pune in partial fulfilment of the requirements for the BS-MS Dual Degree Programme/MSc. Programme/MS-Exit Programme

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