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Transfer principles for integrability and boundedness conditions for motivic exponential functions

Immanuel Halupczok, Raf Cluckers, Julia Gordon
published 2011-11-18

We prove new transfer principles for motivic exponential functions. Where the first such transfer principle of [R. Cluckers, F. Loeser, "Constructible exponential functions, motivic Fourier transform and transfer principle", Ann. Math., 171, 1011-1065 (2010)] treats equalities between integrals, the new transfer principles allow one to change the characteristic of the local field when studying integrability and boundedness conditions. All these transfer principles have applications in the Langlands program. Further we have a theme of results, connecting loci of integrability and loci of boundednes with zero loci and giving new integration results in various settings.

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