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

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