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The Binomial Theorem and motivic classes of universal quasi-split tori

  • Daniel Bergh
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Abstract

Taking symmetric powers of varieties can be seen as a functor from the category of varieties to the category of varieties with an action by the symmetric group. We study a corresponding map between the Grothendieck groups of these categories. In particular, we derive a binomial formula and use it to give explicit expressions for the classes of universal quasi-split tori in the equivariant Grothendieck group of varieties.

Mathematics Subject Classification

14A20 (primary) 14L10 14G27 14M20 (secondary) 

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Notes

Acknowledgements

I would like to thank my advisor, David Rydh, for suggesting several improvements of this text.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCopenhagen UniversityCopenhagen ØDenmark

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