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Conference Paper: Motives of classifying stacks of orthogonal groups
Title | Motives of classifying stacks of orthogonal groups |
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Authors | |
Issue Date | 2014 |
Citation | National Taiwan University Algebraic Geometry Seminar, Taiwan, 2014 How to Cite? |
Abstract | (Based on joint work with Ajneet Dhillon.) The Grothendieck ring of stacks is a dimensional completion of the usual Grothendieck ring of varieties. If $G$ is a linear algebraic group, then its classifying stack has a motivic class $[BG]$ in this ring. The understanding of $[BG]$ is an important problem because of its relevance to the computation of invariants of moduli problems in algebraic geometry. If $G$ is a special algebraic group, such as $GL_n$, $SL_n$ or $Sp_{2n}$, then $[BG]=[G]^{-1}$. For non-special groups, the motive $[BG]$ is much more difficult to understand. In this talk I will describe a solution to this problem for the orthogonal groups. I will also discuss an application of this result to Donaldson-Thomas theory with orientifolds. |
Persistent Identifier | http://hdl.handle.net/10722/256032 |
DC Field | Value | Language |
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dc.contributor.author | Young, MB | - |
dc.date.accessioned | 2018-07-16T07:20:57Z | - |
dc.date.available | 2018-07-16T07:20:57Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | National Taiwan University Algebraic Geometry Seminar, Taiwan, 2014 | - |
dc.identifier.uri | http://hdl.handle.net/10722/256032 | - |
dc.description.abstract | (Based on joint work with Ajneet Dhillon.) The Grothendieck ring of stacks is a dimensional completion of the usual Grothendieck ring of varieties. If $G$ is a linear algebraic group, then its classifying stack has a motivic class $[BG]$ in this ring. The understanding of $[BG]$ is an important problem because of its relevance to the computation of invariants of moduli problems in algebraic geometry. If $G$ is a special algebraic group, such as $GL_n$, $SL_n$ or $Sp_{2n}$, then $[BG]=[G]^{-1}$. For non-special groups, the motive $[BG]$ is much more difficult to understand. In this talk I will describe a solution to this problem for the orthogonal groups. I will also discuss an application of this result to Donaldson-Thomas theory with orientifolds. | - |
dc.language | eng | - |
dc.relation.ispartof | National Taiwan University Algebraic Geometry Seminar | - |
dc.title | Motives of classifying stacks of orthogonal groups | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Young, MB: mbyoung@hku.hk | - |
dc.identifier.hkuros | 243910 | - |
dc.publisher.place | Taiwan | - |