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Curves
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This chapter proves the iso-definability of unit vector C when C is a curve using Riemann-Roch. Recall that a pro-definable set is called iso-definable if it is isomorphic, as a pro-definable set, to a definable set. If C is an algebraic curve defined over a valued field F, then unit vector C is an iso-definable set. The topology on unit vector C is definably generated, that is, generated by a definable family of (iso)-definable subsets. In other words, there is a definable family giving a pre-basis of the topology. The chapter explains how definable types on C correspond to germs of paths on unit vector C. It also constructs the retraction on skeleta for curves. A key result is the finiteness of forward-branching points.
Title: Curves
Description:
This chapter proves the iso-definability of unit vector C when C is a curve using Riemann-Roch.
Recall that a pro-definable set is called iso-definable if it is isomorphic, as a pro-definable set, to a definable set.
If C is an algebraic curve defined over a valued field F, then unit vector C is an iso-definable set.
The topology on unit vector C is definably generated, that is, generated by a definable family of (iso)-definable subsets.
In other words, there is a definable family giving a pre-basis of the topology.
The chapter explains how definable types on C correspond to germs of paths on unit vector C.
It also constructs the retraction on skeleta for curves.
A key result is the finiteness of forward-branching points.
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