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- W2760663313 abstract "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 $FI_mu(s)$ of $mu$, and in particular to a small set of candidate poles for $FI_mu(s)$. We also study various properties of the residue at the largest pole of $FI_mu(s)$. 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." @default.
- W2760663313 created "2017-10-06" @default.
- W2760663313 creator A5031979781 @default.
- W2760663313 date "2017-09-20" @default.
- W2760663313 modified "2023-09-27" @default.
- W2760663313 title "Motivic and p-adic Localization Phenomena" @default.
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- W2760663313 doi "https://doi.org/10.5075/epfl-thesis-8025" @default.
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