The strong Lefschetz principle in algebraic geometry
type: Item
instance of: scholarly article
title: The strong Lefschetz principle in algebraic geometry
zbMATH Open document ID: 0609.14019
DOI: 10.1007/BF01186653
author: Hans-Georg Rück
author: Gerhard Frey
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155146
review text: 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.
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 03C20
Mathematics Subject Classification ID: 13L05
Mathematics Subject Classification ID: 14G99
zbMATH DE Number: 3985408
zbMATH Keywords: ultraproduct
zbMATH Keywords: lifting
zbMATH Keywords: strong Lefschetz principle
zbMATH Keywords: model theory
zbMATH Keywords: curves and their Jacobians
zbMATH Keywords: elementary statements
MaRDI profile type: Publication
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OpenAlex ID: W2083550283
reviewed by: Masayoshi Nagata
description: scientific article; zbMATH DE number 3985408