Shafarevich conjecture

The Shafarevich conjecture concerns the classification of certain geometric objects called algebraic curves, which can be thought of as shapes defined by polynomial equations. It predicts that, for a fixed number of "holes" (genus) and a finite set of "bad" points (places where the shape might be singular), there are only finitely many such curves when considered over a number field, especially with bounded complexity. Essentially, it suggests that, under specific conditions, the diversity of these curves is limited, highlighting a deep connection between algebraic geometry and number theory.