3,179 research outputs found
Endoscopic transfer of orbital integrals in large residual characteristic
This article constructs Shalika germs in the context of motivic integration,
both for ordinary orbital integrals and kappa-orbital integrals. Based on
transfer principles in motivic integration and on Waldspurger's endoscopic
transfer of smooth functions in characteristic zero, we deduce the endoscopic
transfer of smooth functions in sufficiently large residual characteristic.Comment: 33 page
Integrability of oscillatory functions on local fields: transfer principles
For oscillatory functions on local fields coming from motivic exponential
functions, we show that integrability over implies integrability over
for large , and vice versa. More generally, the integrability
only depends on the isomorphism class of the residue field of the local field,
once the characteristic of the residue field is large enough. This principle
yields general local integrability results for Harish-Chandra characters in
positive characteristic as we show in other work. Transfer principles for
related conditions such as boundedness and local integrability are also
obtained. The proofs rely on a thorough study of loci of integrability, to
which we give a geometric meaning by relating them to zero loci of functions of
a specific kind.Comment: 44 page
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