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A linear algebraic group G/ℚ is a subgroup G ⊂ Gln, which is defined as the set of common zeroes of a set of polynomials in the matrix coefficients, where in addition these polynomials have coefficients in ℚ. Of course we cannot take just any set of polynomials, the set has to be somewhat special before its common zeroes form a group. The following examples will clarify what I mean

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Basic Notions and Definitions

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  • 发表日期：

    2025年

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  • Günter Harder

摘要

A linear algebraic group G/ℚ is a subgroup G ⊂ Gln, which is defined as the set of common zeroes of a set of polynomials in the matrix coefficients, where in addition these polynomials have coefficients in ℚ. Of course we cannot take just any set of polynomials, the set has to be somewhat special before its common zeroes form a group. The following examples will clarify what I mean