Related papers: Galois groups of the basic hypergeometric equation…
We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
We compute the first explicit polynomials with Galois groups $G=P\Gamma L_3(4)$, $PGL_3(4)$, $PSL_3(4)$ and $PSL_5(2)$ over $\mathbb{Q}(t)$. Furthermore we compute the first examples of totally real polynomials with Galois groups…
To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call…
We compute the Brauer group of the moduli stack of hyperelliptic curves $\mathcal{H}_g$ over any field of characteristic zero. In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of…
We explicitly compute the ellitpic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.
We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.
We compute explicitly the group of connected components $\pi_0G(\mathbb{R})$ of the real Lie group $G(\mathbb{R})$ for an arbitrary (not necessarily linear) connected algebraic group $G$ defined over the field $\mathbb{R}$ of real numbers.…
An elementary approach to the construction of Coxeter group representations is presented.
We construct \'etale generalized Heisenberg group covers of hyperelliptic curves over number fields. We use these to produce infinite families of quadratic extensions of cyclotomic fields that admit everywhere unramified generalized…
We develop a partial Hopf-Galois theory for partial H-module algebras and we recover analogs of classical results for Hopf algebras.
We give a formula computing the irregular Hodge numbers for a confluent hypergeometric differential equation.
We work over an algebraically closed field of positive characteristic. This paper investigates linear representations of Galois groups arising from wild Galois points on projective hypersurfaces. We prove that these Galois groups lift to…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.
We describe the Galois objects and biGalois groups of monomial nonsemisimple Hopf algebras. The main feature of our description is the use of modified versions of the second cohomology group of the grouplike elements. These computations…
We study a graded Lie algebra arising from the Galois action on the pro-$p$ fundamental group of a once-punctured elliptic curve with complex multiplication. Among other things, we provide a minimal generating set of the rationalized Lie…
A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.
Two Schubert problems on possibly different Grassmannians may be composed to obtain a Schubert problem on a larger Grassmannian whose number of solutions is the product of the numbers of the original problems. This generalizes a…
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…