Obstruction groups for extending deformations of subdiagrams to deformations of diagrams in the categories of ringed topoi and schemes

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Titel
Obstruction groups for extending deformations of subdiagrams to deformations of diagrams in the categories of ringed topoi and schemes
Verfasser
Beutel, Tristan
Gutachter
Rollenske, Sönke ; Christophersen, Jan Arthur
Erschienen
2013
Sprache
Englisch
Dokumenttyp
Dissertation
Schlagwörter
obstructions / cotangent braid / diagrams of ringed topoi / deformation theory / obstruction theory / cotangent complex / diagrams of schemes / deformations / diagrams
URN
urn:nbn:de:hbz:361-26237940

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Abstract

In this thesis we exhibit an obstruction group for the following deformation theoretic problem. Given a diagram and a subdiagram of ringed topoi over a fixed ringed topos $\mathcal{S}$ and given a deformation $\xi$ of the
subdiagram, what is an obstruction group for finding a deformation of the diagram reducing to the given deformation $\xi$ of the subdiagram? We will calculate this obstruction group for a large variety of interesting cases as explicitly as possible. The results hold as well in the case of diagrams and subdiagrams of schemes over a fixed scheme $S$.

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