Related papers: On Shimura subvarieties of the Prym locus

We construct infinitely many abelian surfaces A defined over the rational numbers such that, for a prime ell <= 7, the ell-torsion subgroup of A is not isomorphic as a Galois module to the ell-torsion subgroup of its dual. We do this by…

Let $\overline{\rho}: G_{\mathbf{Q}} \rightarrow {\rm GSp}_4(\mathbf{F}_3)$ be a continuous Galois representation with cyclotomic similitude character -- or, what turns out to be equivalent, the Galois representation associated to the…

The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific…

The Andreotti-Mayer locus is a subset of the moduli space of principally polarized abelian varieties, defined by a condition on the dimension of the singular locus of the theta divisor. It is known that the Jacobian locus in the moduli…

We describe a new construction of families of Galois coverings of the line using basic properties of configuration spaces, covering theory, and the Grauert-Remmert Extension Theorem. Our construction provides an alternative to a previous…

We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…

Given a KHT Shimura variety provided with an action of its unramified Hecke algebra $\mathbb T$, we proved in a previous work, see also the work of Caraiani-Scholze for other PEL Shimura varieties, that its localized cohomology groups at a…

We show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) to the tropical Prym variety of the…

We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group $GSp_6$ compatible when one varies the level at $p$. These classes are expected constituents of an Euler system for the…

We study Kummer varieties attached to 2-coverings of abelian varieties of arbitrary dimension. Over a number field we show that the subgroup of odd order elements of the Brauer group does not obstruct the Hasse principle. Sufficient…

Every GL(2,R)-orbit in hyperelliptic components of strata of abelian differentials in genus greater than two is either closed, dense, or contained in a locus of branched covers.

The first part of the paper gives a new proof of self-duality for Selmer groups: if A is an abelian variety over a number field K, and F/K is a Galois extension with Galois group G, then the Q_pG-representation naturally associated to the…

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 conditionally the non-emptiness for Shimura data associated…

Let $A$ be an abelian variety over a number field $\mathrm E\subset \mathbb C$ and let $\mathbf G$ denote the Mumford--Tate group of $A$. After replacing $\mathrm E$ by a finite extension, the action of the absolute Galois group…

Let $X$ be a smooth projective real algebraic variety. We give new positive and negative results on the problem of approximating a submanifold of the real locus of $X$ by real loci of subvarieties of $X$, as well as on the problem of…

We construct Eigenvarieties for PEL Shimura varieties which interpolate cuspidal, finite slope automorphic forms for PEL Shimura varieties appearing as global sections of (coherent) automorphic sheaves, under the hypothesis that the primes…

For any non-principal polarisation $D$, we explicitly construct $D$-polarised abelian variety $A$, such that its dual abelian variety is not (abstractly) isomorphic to $A$. For $\dim(A)>3$ the construction includes examples with submaximal…

We prove the Mumford--Tate conjecture for those abelian varieties over number fields whose extensions to C have attached adjoint Shimura varieties that are products of simple, adjoint Shimura varieties of certain Shimura types. In…

Let $(R,\mathfrak{m}, k)$ be a strictly local normal $k$-domain of positive characteristic and $P$ be a prime divisor on $X=\text{Spec } R$. We study the Galois category of finite covers over $X$ that are at worst tamely ramified over $P$…

Let $\rho$ be a finite-dimensional faithful representation of a semisimple algebraic group $G$. By means of a deformation argument, we show that there exists a family of Abelian varieties over a smooth and projective curve over the…