The strong Lefschetz principle in algebraic geometry
The strong Lefschetz principle is stated as follows: Assume that a statement A behaves faithfully with respect to constant field extensions (i.e., if \(K_ 1\subset K_ 2\) are algebraically closed fields and A a statement about \(K_ 1\) and if A is true over \(K_ 2\), then A is true over \(K_ 1)\) and if A is true over an algebraically closed field, then A is true over all algebraically closed fields of the same characteristic. Of course this is not valid for all A. But, if A is expressed as an elementary statement, then the principle is valid, as is known by model theory. The authors apply this to several cases in algebraic geometry, namely, they give several statements related with curves and their Jacobians, which are equivalent to elementary statements.
scientific article; zbMATH DE number 3985408