On Rigid, Hard and Soft Problems and Results in Arithmetic Geometry

Rigid, hard and soft problems and results in arithmetic geometry are presented. “Soft” and “hard” in our paper are limited to the framework of solutions of quadratic forms over rings of integers of local and global fields, the Hardy-Littlewood-Kloosterman method. Next we consider the notion of rigidity. In the framework we give review of some novel results in the aria.