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Equivariant motivic integration and proof of the integral identity conjecture for regular functions

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Abstract

We develop Denef–Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ring defined in this article is more elementary and it yields the application to the conjecture.

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Acknowledgements

This article was partially written during the authors’ visits to Department of Mathematics-KU Leuven in December 2017 and Vietnam Institute for Advanced Studies in Mathematics in January 2018. The authors thank sincerely these institutions for excellent atmospheres and warm hospitalities.

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Authors and Affiliations

  1. Faculty of Mathematics, Mechanics and Informatics, VNU University of Science, Vietnam National University, Hanoi, Hanoi, Vietnam

    Quy Thuong Lê

  2. Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009, Bilbao, Bizkaia, Spain

    Hong Duc Nguyen

  3. TIMAS, Thang Long University, Nghiem Xuan Yem, Hanoi, Vietnam

    Hong Duc Nguyen

Authors
  1. Quy Thuong Lê
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  2. Hong Duc Nguyen
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Correspondence to Quy Thuong Lê.

Additional information

Communicated by Vasudevan Srinivas.

Dedicated to Professor Gert-Martin Greuel on the occasion of his seventy-fifth birthday.

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Lê Quy Thuong research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number FWO.101.2015.02. Nguyen Hong Duc research is partially supported by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718, by the ERCEA Consolidator Grant 615655 NMST and by Juan de la Cierva Incorporación IJCI-2016-29891.

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Lê, Q.T., Nguyen, H.D. Equivariant motivic integration and proof of the integral identity conjecture for regular functions. Math. Ann. 376, 1195–1223 (2020). https://doi.org/10.1007/s00208-019-01940-2

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  • DOI: https://doi.org/10.1007/s00208-019-01940-2

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