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Journal für die reine und angewandte Mathematik

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Volume 2018, Issue 735


The motivic Thom–Sebastiani theorem for regular and formal functions

Quy Thuong Lê
Published Online: 2015-06-16 | DOI: https://doi.org/10.1515/crelle-2015-0022


Thanks to the work of Hrushovski and Loeser on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom–Sebastiani theorem in the case of regular functions. Moreover, slightly extending Hrushovski–Loeser’s construction adjusted to Sebag, Loeser and Nicaise’s motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich–Soibelman’s theory of motivic Donaldson–Thomas invariants.


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About the article

Received: 2014-05-28

Published Online: 2015-06-16

Published in Print: 2018-02-01

Funding Source: H2020 European Research Council

Award identifier / Grant number: 246903/NMNAG

The author is partially supported by the Centre Henri Lebesgue (program “Investissements d’avenir”, ANR-11-LABX-0020-01) and by ERC under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement no. 246903/NMNAG.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 735, Pages 175–198, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0022.

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