6 citations · 17 across the 8 of their papers we have counts for
11 papers
Integral points on coarse Hilbert moduli schemes
Rafael von Kanel, Arno Kret
We continue our study of integral points on moduli schemes by combining the method of Faltings (Arakelov, Parsin, Szpiro) with modularity results and Masser-Wüstholz isogeny estima…
On the central value of Rankin -functions for self-dual algebraic representations of linear groups over totally real fields
Laurent Clozel, Arno Kret
Deligne has formulated extremely influential conjectures about certain special values of the -functions of (Grothendieck) motives over a number field . Given the conjectural…
of Igusa varieties via automorphic forms
Arno Kret, Sug Woo Shin
Our main theorem describes the degree 0 cohomology of Igusa varieties in terms of one-dimensional automorphic representations in the setup of mod p Hodge-type Shimura varieties wit…
Galois representations for even general special orthogonal groups
Arno Kret, Sug Woo Shin
We prove the existence of -valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\…
Integral points on Hilbert moduli schemes
Rafael von Kanel, Arno Kret
We use the method of Faltings (Arakelov, Paršin, Szpiro) in order to explicitly study integral points on a class of varieties over called Hilbert moduli schemes. For in…
Galois representations for general symplectic groups
Arno Kret, Sug Woo Shin
We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real num…
Equidistribution in supersingular Hecke orbits
Arno Kret
We prove an equidistribution result for Hecke operators acting on the basic stratum of certain Shimura varieties. We relate the rate of convergence to the bounds from the Ramanujan…
Combinatorics of the basic stratum
Arno Kret
We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura…
The trace formula and the existence of PEL type Abelian varieties modulo p
Arno Kret
We show, using the trace formula, that any Newton stratum of a Shimura variety of PEL-type of types (A) and (C) is non-empty at the primes of good reduction. Furthermore we prove c…
Existence of cuspidal representations of p-adic reductive groups
Arno Kret
We prove that any reductive group G over a non-Archimedean local field has a cuspidal complex representation.
The basic stratum of some simple Shimura varieties
Arno Kret
Under simplifying hypotheses we prove a relation between the l-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex…