Related papers: Dimensions of Prym Varieties

A p-divisible group over a complete local domain determines a Galois representation on the Tate module of its generic fibre. We determine the image of this representation for the universal deformation in mixed characteristic of a…

We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick-Brown, we define a new invariant called the weighted…

Let F be a number field with adele ring A_F, and \pi an isobaric, algebraic automorphic representation of GL_4(A_F) of a fixed archimedean weight, which is quasi-regular, meaning that at every archimedean place v of F, the 4-dimensional…

We define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of…

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…

We prove an extension of the Babbage-Enriques-Petri theorem for semi-canonical curves. We apply this to show that the Prym variety of a generic element of a codimension $k$ subvariety of $\mathcal{R}_{g}$ is not isogenous to another…

In this paper, we study the Galois representations attached to products of Drinfeld modules. As an analogue of Serre's classical result on the images of Galois representations associated with products of elliptic curves, we prove that for…

Let $p>5$ be a prime integer and $K/\mathbb{Q}_p$ a finite ramified extension with ring of integers $\mathcal{O}$ and uniformizer $\pi$. Let $n>1$ be a positive integer and $\rho_n:G_\mathbb{Q} \to \text{GL}_2(\mathcal{O}/\pi^n)$ be a…

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…

We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because…

We prove that Prym varieties of algebraic curves with two smooth fixed points of involution are exactly the indecomposable principally polarized abelian varieties whose theta-functions provide explicit formulae for integrable 2D…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

To a finite group $G$, one can associate several notions of dimensions (or degrees). In this survey, we attempt to bring together some of the notions of dimensions or degrees defined using representations of the group in General Linear…

Let G be a simple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Let \sigma:G->G be a strict endomorphism (i. e., the subgroup G(\sigma) of \sigma-fixed points is finite). Also,…

The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…

We compare the dimensions of the irreducible Sp(2g,K)-modules over a field K of characteristic p constructed by Gow with the dimensions of the irreducible Sp(2g,F_p)-modules that appear in the first approximation to representations of…

We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…

We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil transfers of generalized Severi-Brauer varieties. We then…

For a group $G$ acting on an affine variety $X$, the separating variety is the closed subvariety of $X\times X$ encoding which points of $X$ are separated by invariants. We concentrate on the indecomposable rational linear representations…

This paper proves the branching laws for the full class of unitarizable representations of general linear groups in non-Archimedean local fields, extending the original notion of Gan-Gross-Prasad relevant pair for Arthur-type…