203 research outputs found
Compactification of Drinfeld modular varieties and Drinfeld Modular Forms of Arbitrary Rank
We give an abstract characterization of the Satake compactification of a
general Drinfeld modular variety. We prove that it exists and is unique up to
unique isomorphism, though we do not give an explicit stratification by
Drinfeld modular varieties of smaller rank which is also expected. We construct
a natural ample invertible sheaf on it, such that the global sections of its
-th power form the space of (algebraic) Drinfeld modular forms of weight
. We show how the Satake compactification and modular forms behave under all
natural morphisms between Drinfeld modular varieties; in particular we define
Hecke operators. We give explicit results in some special cases
Compactification of a Drinfeld Period Domain over a Finite Field
We study a certain compactification of the Drinfeld period domain over a
finite field which arises naturally in the context of Drinfeld moduli spaces.
Its boundary is a disjoint union of period domains of smaller rank, but these
are glued together in a way that is dual to how they are glued in the
compactification by projective space. This compactification is normal and
singular along all boundary strata of codimension . We study its geometry
from various angles including the projective coordinate ring with its Hilbert
function, the cohomology of twisting sheaves, the dualizing sheaf, and give a
modular interpretation for it. We construct a natural desingularization which
is smooth projective and whose boundary is a divisor with normal crossings. We
also study its quotients by certain finite groups
Adelic Openness for Drinfeld Modules in Special Characteristic
For any Drinfeld module of special characteristic p0 over a finitely
generated field, we study the associated adelic Galois representation at all
places different from p0 and \infty, and determine the image of the geometric
Galois group up to commensurability
- …