Clifton Cunningham

Good orbital integrals

This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is based on motivic integration, works both in characteristic zero and in positive characteristic. As an application, the Fundamental Lemma for this class of integrals is lifted from positive characteristic to characteristic zero. The results are based on a formula for orbital integrals as distributions inflated from orbits in the quotient spaces of the Moy-Prasad filtrations of the Lie algebra. This formula is established by Fourier analysis on these quotient spaces.

On the computability of some positive-depth supercuspidal characters near the identity

This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of

Computing Genus-2 Hilbert–Siegel Modular Forms over via the Jacquet–Langlands Correspondence

p

Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group

-adic symplectic and special orthogonal groups, near the identity element. We declare two representations equivalent if their characters coincide on a specific neighbourhood of the identity (which is larger than the neighbourhood on which Harish-Chandra local character expansion holds). We construct a parameter space

FROM THE FUNCTION-SHEAF DICTIONARY TO QUASICHARACTERS OF -ADIC TORI

B

Motivic Proof of a Character Formula for SL(2)

(that depends on the group and a real number

A NOTE ON L-PACKETS AND ABELIAN VARIETIES OVER LOCAL FIELDS

r>0

Report from the Ambassador to Cida-2.

) for the set of equivalence classes of the representations of minimal depth

CHARACTER SHEAVES OF ALGEBRAIC GROUPS DEFINED OVER NON-ARCHIMEDEAN LOCAL FIELDS

r

Isogeny Classes of Hilbert–Blumenthal Abelian Varieties over Finite Fields

satisfying some additional assumptions. This parameter space is essentially a geometric object defined over