510 research outputs found
Representation Growth and Rational Singularities of the Moduli Space of Local Systems
We relate the asymptotic representation theory of and
the singularities of the moduli space of -local systems on a smooth
projective curve, proving new theorems about both. Regarding the former, we
prove that, for every d, the number of n-dimensional representations of
grows slower than , confirming a conjecture of
Larsen and Lubotzky. Regarding the latter, we prove that the moduli space of
-local systems on a smooth projective curve of genus at least 12 has
rational singularities. Most of our results apply more generally to semi-simple
algebraic groups.
For the proof, we study the analytic properties of push forwards of smooth
measures under algebraic maps. More precisely, we show that such push forwards
have continuous density if the algebraic map is flat and all of its fibers have
rational singularities.Comment: preliminary version, comments are welcome. v2. Revised version, now
covering all semi simple group
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
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