Some minimisation algorithms in arithmetic invariant theory

Arithmetic invariant theory

Arithmetic invariant theory II

2 Lifting results 4 2.1 Pure inner forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Twisting the representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Rational orbits in the twisted representation . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 A cohomological obstruction to lifting invariants . . . . . . . . . . . . . . . ...

Some Problems in Invariant Theory

We present summaries of a number of research problems in invariant theory. These problems were posed during the organized problem sessions held during the April 2002, Kingston Ontario, Invariant Theory Workshop and Conference.

Arithmetic Teichmuller Theory

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

Arithmetic Deformation Theory of Lie Algebras

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...