Related papers: Hypergeometric Galois Actions
We discuss the following two problems: 1) The properties of the multiple zeta-values and their generalizations, multiple polylogarithms at N-th roots of unity; 2) The action of the absolute Galois group on the pro-l-completion of the…
We examine a moduli problem for real and quaternionic vector bundles on a smooth complex projective curve with a fixed real structure, and we give a gauge-theoretic construction of moduli spaces for semi-stable such bundles with fixed…
A global action is an algebraic analogue of a topological space. It consists of group actions $G_\alpha\curvearrowright X_\alpha$, $(\alpha\in\Phi)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of…
Proposing a certain category of bialgebroid maps we show that the balanced depth 2 extensions appear as they were the finitary Galois extensions in the context of quantum groupoid actions, i.e., actions by finite bialgebroids, weak…
We define the notion of a $G$-structure for elliptic curves, where $G$ is a finite 2-generated group. When $G$ is abelian, a $G$-structure is the same as a classical congruence level structure. There is a natural action of…
We consider the stack of stable curves of genus g with a given dual graph and we give an explicit desingularization of its closure in the moduli stack of stable curves. We study in particular the one-dimensional substack of curves with at…
In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…
We gives an explicit genus 3 curve over Q such that the Galois action on the torsion points of its Jacobian is a large as possible. That such curves exist is a consequence of a theorem of D. Zureick-Brown and the author; however, those…
This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…
The class-invariant homomorphism allows one to measure the Galois module structure of extensions obtained by dividing points on abelian varieties. In this paper, we consider the case when the abelian variety is the Jacobian of a Fermat…
We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon…
This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we describe in detail four rigidity results that concern actions of…
We introduce a systematic method to derive the effective action for domain walls directly from the scalar field theory that gives rise to their solitonic solutions. The effective action for the Goldstone mode, which characterizes the…
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…
We provide an account of the construction of the moduli stack of elliptic curves as an analytic orbifold. While intimately linked to Thurston's point of view on the subject (discrete groups acting properly and effectively on differentiable…
We define comodule algebras and Galois extensions for actions of bialgebroids. Using just module conditions we characterize the Frobenius extensions that are Galois as depth two and right balanced extensions. As a corollary, we obtain…
Suppose we are given a profinite group $G$ acting on a formal moduli stack $\mathcal{M}$, and we want to understand the group action, and compute cohomology related to this group action. How can we do it? This prolegomenon surveys two…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
Some conditions for the Galois map to be injective are given in the groupoid acting on a noncommutative ring context. In the particular case in which the Galois extension is a central Galois algebra, it is given a complete characterization…
We examine a class of N=2 supersymmetric gauge theories in (3+1) dimensions whose Lagrangians are determined by graphs consisting of two building blocks, namely a tri-vertex and a line. A line represents an SU(2) gauge group and a…