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Jim Humphreys
Jim Humphreys
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As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 paper. This paper is probably most readily found in the first volume of Weil's papers published by Springer, but the later book presents his notion of variety and the related field theory (with generic points) in far more detail.

What I'd like to add is a reference to Dieudonne's book History of Algebraic Geometry (especially VII.4). This was first published in French in 1974 and then in English translation in 1985. Dieudonne took a strong interest in this kind of history and assembled a lot of material about older origins of ideas while emphasizing the key role played by Weil. Naturally names like Mvan der Waerden, E. Noether, and Siegel are part of that history as well.

As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 paper. This paper is probably most readily found in the first volume of Weil's papers published by Springer, but the later book presents his notion of variety and the related field theory (with generic points) in far more detail.

What I'd like to add is a reference to Dieudonne's book History of Algebraic Geometry (especially VII.4). This was first published in French in 1974 and then in English translation in 1985. Dieudonne took a strong interest in this kind of history and assembled a lot of material about older origins of ideas while emphasizing the key role played by Weil. Naturally names like M. Noether and Siegel are part of that history as well.

As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 paper. This paper is probably most readily found in the first volume of Weil's papers published by Springer, but the later book presents his notion of variety and the related field theory (with generic points) in far more detail.

What I'd like to add is a reference to Dieudonne's book History of Algebraic Geometry (especially VII.4). This was first published in French in 1974 and then in English translation in 1985. Dieudonne took a strong interest in this kind of history and assembled a lot of material about older origins of ideas while emphasizing the key role played by Weil. Naturally names like van der Waerden, E. Noether, and Siegel are part of that history as well.

Source Link
Jim Humphreys
Jim Humphreys
  • 52.9k
  • 4
  • 120
  • 240

As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 paper. This paper is probably most readily found in the first volume of Weil's papers published by Springer, but the later book presents his notion of variety and the related field theory (with generic points) in far more detail.

What I'd like to add is a reference to Dieudonne's book History of Algebraic Geometry (especially VII.4). This was first published in French in 1974 and then in English translation in 1985. Dieudonne took a strong interest in this kind of history and assembled a lot of material about older origins of ideas while emphasizing the key role played by Weil. Naturally names like M. Noether and Siegel are part of that history as well.