Don Blasius

On multiplicities for SL(n)

We use the strong Artin conjecture for Galois extensions of Heisenberg type to show that a cuspidal automorphic representation of SL(N)/F, forF a number field andN>2, can occur with multiplicity greater than one. We also exhibit two cuspidalL-packets (forF=Q andN prime) which are locally isomorphic for primesp different fromN, but which are disjoint atN, i.e. thatL-packets are not rigid.

Cohomology of Congruence Subgroups of SU (2, 1) p and Hodge Cycles on Some Special Complex Hyperbolic Surfaces

Let G be a semisimple algebraic group over a number field F and set G ∞ = ∏ v∈S ∞ Gv, where S∞ is the set of archimedean places of F. As is well-known, the cohomology of a cocompact lattice Γ ⊂ G ∞ is expressed in terms of the decomposition

Motives for Hilbert modular forms

{L^2}\left( {\Gamma \backslash {G_\infty }} \right) \simeq \hat \oplus m(\pi ,\Gamma )\pi

Tate classes and arithmetic quotients of the two-ball

In this paper we study the action of complex conjugation on Shimura varieties and the problem of descending these to the maximal totally real field of the reflex field. We prove the existence of such descent for many Shimura varieties whose associated adjoint group has certain factors of type A or D. This includes a large family of Shimura varieties of abelian type. Our considerations and constructions are carried out purely at the level of Shimura data and group theory.