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DC Field | Value | Language |
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dc.contributor.author | Roy, Biman | - |
dc.date.accessioned | 2024-12-27T11:05:49Z | - |
dc.date.available | 2024-12-27T11:05:49Z | - |
dc.date.issued | 2024-12 | - |
dc.identifier.citation | 123p. | en_US |
dc.identifier.uri | http://hdl.handle.net/10263/7485 | - |
dc.description | This thesis is under the supervision of Dr.Utsav Choudhury | en_US |
dc.description.abstract | Morel-Voevodsky developed A^1-homotopy theory which is a bridge between algebraic geometry and algebraic topology. In this thesis we study the A^1-connected component of a smooth variety in great detail. We have shown that the A^1-connected component of a smooth variety contains the information about the existence of affine lines in the variety. Using this and Miyanishi-Sugie's algebraic characterisation, we determine that the affine plane is the only A^1-contractible smooth affine surface over the field of characteristic zero. In the other part of the thesis, we studied the A^1-homotopy type of A^2-{(0,0)}. We showed that over the field of characteristic zero, if an open subvariety of a smooth affine surface is A^1-weakly equivalent to A^2-{(0,0)}, then it is isomorphic to A^2-{(0,0)}. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Indian Statistical Institute, Kolkata | en_US |
dc.relation.ispartofseries | ISI Ph. D Thesis;TH | - |
dc.subject | A^1-homotopy theory | en_US |
dc.subject | Affine algebraic geometry | en_US |
dc.subject | Zariski Cancellation | en_US |
dc.title | A1-homotopy types of A2 and A2 \ {(0, 0)} | en_US |
dc.type | Thesis | en_US |
Appears in Collections: | Theses |
Files in This Item:
File | Description | Size | Format | |
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thesis_Biman Roy-24-12-24.pdf | Thesis | 1.41 MB | Adobe PDF | View/Open |
form 17-Biman Roy-24-12-24.pdf | Form 17 | 683.17 kB | Adobe PDF | View/Open |
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