Motivic and $p$-adic Localization Phenomena
Autor: | Wyss, Dimitri |
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Rok vydání: | 2017 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the $p$-adic pushforward of the Haar measure under a hypertoric moment map $\mu$. This leads to an explicit formula for the Igusa zeta function $I_\mu(s)$ of $\mu$, and in particular to a small set of candidate poles for $I_\mu(s)$. We also study various properties of the residue at the largest pole of $I_\mu(s)$. Finally, if $\mu$ is constructed out of a quiver $\Gamma$ we give a conjectural description of this residue in terms of indecomposable representations of $\Gamma$ over finite depth rings. The connections between these different results is the method of proof. At the heart of each theorem lies a motivic or $p$-adic volume computation, which is only possible due to some surprising cancellations. These cancellations are reminiscent of a result in classical symplectic geometry by Duistermaat and Heckman on the localization of the Liouville measure, hence the title of the thesis. Comment: Thesis |
Databáze: | arXiv |
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