7,071 research outputs found
An example of non-homeomorphic conjugate varieties
We give examples of smooth quasi-projective varieties over complex numbers,
in the context of connected Shimura varieties, which are not homeomorphic to a
conjugate of itself by an automorphism of the complex numbers.Comment: 4 page
Unique decomposition of tensor products of irreducible representations of simple algebraic groups
We show that a tensor product of irreducible, finite dimensional
representations of a simple Lie algebra over a field of characteristic zero,
determines the individual constituents uniquely. This is analogous to the
uniqueness of prime factorisation of natural numbers.Comment: 23 pages, to appear in Annals of Mathematic
On strong multiplicity one for automorphic representations
We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro
and Shalika. Let be a unitary, cuspidal, automorphic representation of
GL_n(\A_K). Let be a set of finite places of , such that the sum
is convergent. Then is uniquely determined
by the collection of the local components of . Combining this theorem with base change, it is
possible to consider sets of positive density, having appropriate splitting
behavior with respect to solvable extensions of , and where is
determined upto twisting by a character of the Galois group of over .Comment: 8 page
On the vanishing of the measurable Schur cohomology groups of Weil groups
We generalize a theorem of Tate and show that the second cohomology of the
Weil group of a global or local field with coefficients in \C^* (or more
generally, with coefficients in the complex points of a tori over \C) vanish,
where the cohomology groups are defined using measurable cochains in the sense
of Moore. We recover a theorem of Labesse proving that admissible homomorphisms
of a Weil group to the Langlands dual of a reductive group can be lifted to an
extension of the Langlands dual group by a tori.Comment: To appear in Compositio Mathematica. Minor editing, and a conjecture
in the earlier version on the vanishing of the higher cohomology groups of
Weil groups is fals
Recovering modular forms and representations from tensor and symmetric powers
We consider the problem of determining the relationship between two
representations knowing that some tensor or symmetric power of the original
represetations coincide. Combined with refinements of strong multiplicity one,
we show that if the characters of some tensor or symmetric powers of two
absolutely irreducible -adic representation with the algebraic envelope of
the image being connected, agree at the Frobenius elements corresponding to a
set of places of positive upper density, then the representations are twists of
each other by a finite order character.Comment: 18 pages; this is a revised version of a paper submitted to the old
Number Theory archive as ANT-035
- β¦