Related papers: N\'eron models and base change
We prove the existence of abelian varieties not isogenous to Jacobians over characterstic $p$ function fields. Our methods involve studying the action of degree $p$ Hecke operators on hypersymmetric points, as well as their effect on the…
The cones of divisors and curves defined by various positivity conditions on a smooth projective variety have been the subject of a great deal of work in algebraic geometry, and by now they are quite well understood. However the analogous…
The parity violation programs at MIT-Bates, Jefferson Lab and Mainz are presently focused on developing a better understanding of the sea-quark contributions to the vector matrix elements of nucleon structure. The success of these programs…
We consider the curves $y^2=x^{2^m} -1$ and $y^2=x^{2^{d}+1}-x$ over the rationals. These curves are related via their associated Jacobian varieties in that the Jacobians of the latter appear as factors of the Jacobians of the former. One…
Using the method developed in {\tt hep-th/0103015}, we determine the non-abelian Born-Infeld action through ${\cal O}(\alpha'{}^3)$. We start from solutions to a Yang-Mills theory which define a stable holomorphic vector bundle.…
We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2…
We construct an ${\cal N}{=}\,2$ supersymmetric extension of $n$-particle Ruijsenaars-Schneider models. The guiding feature is a deformation of the phase space. The supercharges have a "free" form linear in the fermions but produce an…
Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of…
We investigate non-perturbative features of a three-dimensional Abelian Higgs model with singly- and doubly-charged scalar fields coupled to a single compact Abelian gauge field. The model is pretending to describe various planar systems of…
Faltings proved that there are finitely many abelian varieties of genus $g$ over a number field $K$, with good reduction outside a finite set of primes $S$. Fixing one of these abelian varieties $A$, we prove that there are finitely many…
The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is…
A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved…
The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N…
Based on the construction of Poisson-Lie T-dual $\sigma$-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T-duality group. This group generalises the well-known abelian T-duality group…
We characterize stable curves $X$ whose compactified degree-$d$ Jacobian is of N\'eron type. This means the following: for any one-parameter regular smoothing of $X$, the special fiber of the N\'eron model of the Jacobian of the generic…
We propose a generalization of the color codes based on finite groups $G$. For non-abelian groups, the resulting model supports non-abelian anyonic quasiparticles and topological order. We examine the properties of these models such as…
We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 2 an abelian semigroup G of GL(n;C) generated by n + 1…
In this paper we study the \'etale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable…
The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change…
We show that any polarized abelian variety over a finite field is covered by a Jacobian whose dimension is bounded by an explicit constant. We do this by first proving an effective version of Poonen's Bertini theorem over finite fields,…