59 citations · 137 across the 24 of their papers we have counts for
24 papers · 1 filter
Bézout's theorem for abelian varieties
Olivier Debarre, Ben Moonen
Let , be closed irreducible subvarieties of an absolutely simple abelian variety of dimension over a field. If , we prove that the addition morp…
Integral aspects of Fourier duality for abelian varieties
Junaid Hasan, Hazem Hassan, Milton Lin +3
We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If is smooth quasi-p…
A remark on the paper of Deninger and Murre
Ben Moonen
We show that the results proven by Deninger and Murre directly imply that the Chern classes of the de Rham bundle of an abelian scheme are torsion elements in the Chow ring, a resu…
A classification of Shimura curves in
Ben Moonen
We give a precise classification, in terms of Shimura data, of all 1-dimensional Shimura subvarieties of a moduli space of polarized abelian varieties.
The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic
Lie Fu, Ben Moonen
We study Gushel-Mukai (GM) varieties of dimension 4 or 6 in characteristic . Our main result is the Tate conjecture for all such varieties over finitely generated fields of char…
Algebraic cycles on Gushel-Mukai varieties
Lie Fu, Ben Moonen
We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conje…
Computing discrete invariants of varieties in positive characteristic. I. Ekedahl-Oort types of curves
Ben Moonen
We develop a method to compute the Ekedahl-Oort type of a curve C over a field k of characteristic p (which is the isomorphism type of the p-kernel group scheme J[p], where J is th…
The Coleman-Oort conjecture: reduction to three key cases
Ben Moonen
We show that the Coleman-Oort conjecture can be reduced to three particular cases. As an application we extend a result of Lu and Zuo, to the effect that for g at least 8 the Colem…
A note on images of Galois representations (with an application to a result of Litt)
Anna Cadoret, Ben Moonen
Let be a variety (possibly non-complete or singular) over a finitely generated field of characteristic . For a prime number , let be the Galois representa…
A remark on the Tate conjecture
Ben Moonen
The Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations, and an assertion (T) which says that every Tate class is algebraic. We show that…
The Deligne-Mostow list and special families of surfaces
Ben Moonen
We study whether there exist infinitely many surfaces with given discrete invariants for which the H^2 is of CM type. This is a surface analogue of a conjecture of Coleman about cu…
Integral and adelic aspects of the Mumford-Tate conjecture
Anna Cadoret, Ben Moonen
Let be an abelian variety over a subfield that is of finite type over . We prove that if the Mumford-Tate conjecture for is true, then al…
On the Tate and Mumford-Tate conjectures in codimension one for varieties with h^{2,0}=1
Ben Moonen
We prove the Tate conjecture for divisor classes and the Mumford-Tate conjecture for the cohomology in degree 2 for varieties with over a finitely generated field of ch…
Some remarks on modified diagonals
Ben Moonen, Qizheng Yin
We prove a number of basic vanishing results for modified diagonal classes. We also obtain some sharp results for modified diagonals of curves and abelian varieties, and we prove a…
On a question of O'Grady about modified diagonals
Ben Moonen, Qizheng Yin
Let X be an abelian variety of dimension g. In a recent preprint O'Grady defines modified diagonal classes Γ^m on X^m and he conjectures that the class of Γ^m in the Chow ring of X…
The Torelli locus and special subvarieties
Ben Moonen, Frans Oort
We study the Torelli locus T_g in the moduli space A_g of abelian varieties. We consider special subvarieties (Shimura subvarieties) contained in the Torelli locus. We review the c…
On the Chow motive of an abelian scheme with non-trivial endomorphisms
Ben Moonen
Let X be an abelian scheme over a base variety S with endomorphism algebra D. We prove that the relative Chow motive R(X/S) has a canonical decomposition as a direct sum of motives…
Special subvarieties arising from families of cyclic covers of the projective line
Ben Moonen
We consider families of cyclic covers of the projective line, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are preci…
Divided powers in Chow rings and integral Fourier transforms
Ben Moonen, Alexander Polishchuk
We prove that for any monoid scheme M over a field with proper multiplication maps from M x M to M, we have a natural PD-structure on the ideal CH_{>0}(M) of CH(M) with regard to t…
Relations between tautological cycles on Jacobians
Ben Moonen
We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, eas…
Discrete invariants of varieties in positive characteristic
B. Moonen, T. Wedhorn
If is a scheme of characteristic , we define an -zip over to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded…
A dimension formula for Ekedahl-Oort strata
Ben Moonen
We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by cosets in a Weyl group. The main result of this paper is that the dimension of a st…
Serre-Tate Theory for Moduli Spaces of PEL Type
Ben Moonen
The main goal of this paper is to generalize Serre-Tate theory of "ordinary" local moduli to Shimura varieties of PEL type. To this end we develop a generalized notion of ordinarin…
Hodge classes on abelian varieties of low dimension
B. J. J. Moonen, Yu. G. Zarhin
In this paper we study Hodge classes on complex abelian varieties. We prove some general results that allow us, in certain cases, to compute the Hodge group of a product abelian va…