6 citations · 10 across the 6 of their papers we have counts for
11 papers
Trivializing Torsors for Difference Algebraic Groups
Annette Bachmayr, Michael Wibmer
We study torsors for groups defined by algebraic difference equations. Our main result provides necessary and sufficient conditions on the base difference field for all such torsor…
On homomorphic encryption using abelian groups: Classical security analysis
Eleni Agathocleous, Vishnupriya Anupindi, Annette Bachmayr +3
In [15], Leonardi and Ruiz-Lopez propose an additively homomorphic public key encryption scheme whose security is expected to depend on the hardness of the learning homomorphism wi…
The differential Galois group of the rational function field
Annette Bachmayr, David Harbater, Julia Hartmann +1
We determine the absolute differential Galois group of the field of rational functions: It is the free proalgebraic group on a set of cardinality . Th…
Algebraic groups as difference Galois groups of linear differential equations
Annette Bachmayr, Michael Wibmer
We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field with derivation …
Free differential Galois groups
Annette Bachmayr, David Harbater, Julia Hartmann +1
We study the structure of the absolute differential Galois group of a rational function field over an algebraically closed field of characteristic zero. In particular, we relate th…
Large Fields in Differential Galois Theory
Annette Bachmayr, David Harbater, Julia Hartmann +1
We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over . More generally, we sh…
Differential Embedding Problems over Laurent series fields
Annette Bachmayr, David Harbater, Julia Hartmann
We solve the inverse differential Galois problem over the fraction field of and use this to solve split differential embedding problems over that are induced…
Differential Embedding Problems over Complex Function Fields
Annette Bachmayr, David Harbater, Julia Hartmann +1
We introduce the notion of differential torsors, which allows the adaptation of constructions from algebraic geometry to differential Galois theory. Using these differential torsor…
Torsors for Difference Algebraic Groups
Annette Bachmayr, Michael Wibmer
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors…
New classes of parameterized differential Galois groups
Annette Bachmayr
This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois groups over K(x) eve…
Differential Galois Groups over Laurent Series Fields
David Harbater, Julia Hartmann, Annette Maier
In this manuscript, we apply patching methods to give a positive answer to the inverse differential Galois problem over function fields over Laurent series fields of characteristic…