Re:New Shape Opens ‘Wormhole’ Between Numbers and Geometry
by langlands on Monday July 19, 2021 @07:25PM
(#27888429)
Unfortunately the "geometry" involved is not the kind of geometry that lends itself towards being easily drawn to give understanding.
If you had to draw a picture of it, it would just be a sphere (since it shares many properties with a genus 0 complex curve).
But it's a very different beast than usual geometric shapes. A lot of modern number theory is motivated by an analogy between "p and t", where t is a parameter in a polynomial like t^2 - 2, and where p is a prime number. This space takes the analogy to an extreme where p literally is the parameter for the space[0], like t would be a parameter for the real line.
[0]Not exactly true - true for the "disk" cover of the FF curve.
If you had to draw a picture of it, it would just be a sphere (since it shares many properties with a genus 0 complex curve).
But it's a very different beast than usual geometric shapes. A lot of modern number theory is motivated by an analogy between "p and t", where t is a parameter in a polynomial like t^2 - 2, and where p is a prime number. This space takes the analogy to an extreme where p literally is the parameter for the space[0], like t would be a parameter for the real line.
[0]Not exactly true - true for the "disk" cover of the FF curve.