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What is an $F$-rational section of a line bundle?
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Let $X$ be an algebraic variety over a field $F$. What is the definition of an ``$F$-rational section" of a line bundle? I can't find any references for this notion.
algebraic-geometry
asked Jul 25 at 21:50
Mehta
34519
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up vote
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Let $X$ be an algebraic variety over a field $F$. What is the definition of an ``$F$-rational section" of a line bundle? I can't find any references for this notion.
algebraic-geometry
asked Jul 25 at 21:50
Mehta
34519
1
It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let $X$ be an algebraic variety over a field $F$. What is the definition of an ``$F$-rational section" of a line bundle? I can't find any references for this notion.
algebraic-geometry
asked Jul 25 at 21:50
Mehta
34519
Let $X$ be an algebraic variety over a field $F$. What is the definition of an ``$F$-rational section" of a line bundle? I can't find any references for this notion.
algebraic-geometry
asked Jul 25 at 21:50
Mehta
34519
asked Jul 25 at 21:50
Mehta
34519
asked Jul 25 at 21:50
Mehta
34519
asked Jul 25 at 21:50
Mehta
34519
34519
1
It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02
add a comment |Â
1
It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02
1
1
It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02
It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02
add a comment |Â
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It might help if you could give some context - but I suspect here it's saying you have a morphism of $F$-schemes $Xrightarrow L$ (i.e. a section in the usual sense). The reason for this distinction, at least in the context I've seen, is that sometimes people work after base changing to the algebraic closure.
– loch
Jul 26 at 0:02