Title: Effective height bounds for odd-degree totally real points on some curves.
Speaker: Levent Alpoge (Harvard University)
Speaker's URL: https://people.math.harvard.edu/~alpoge/
Abstract: I will give a finite-time algorithm that, on input (g,K,S) with g > 0, K a totally real number field of odd degree, and S a finite set of places of K, outputs the finitely many g-dimensional abelian varieties A/K which are of GL_2-type over K and have good reduction outside S.
The point of this is to effectively compute the S-integral K-points on a Hilbert modular variety, and the point of that is to be able to compute all K-rational points on complete curves inside such varieties.
This gives effective height bounds for rational points on infinitely many curves and (for each curve) over infinitely many number fields. For example one gets effective height points for odd-degree totally real points on x^6 + 4y^3 = 1, by using the hypergeometric family associated to the arithmetic triangle group \Delta(3,6,6).
Effective height bounds for odd-degree totally real points on some curves
November 29, 2021
4:15PM - 5:15PM
Zoom (email organizers for link)
Add to Calendar
2021-11-29 17:15:00
2021-11-29 18:15:00
Effective height bounds for odd-degree totally real points on some curves
Title: Effective height bounds for odd-degree totally real points on some curves.
Speaker: Levent Alpoge (Harvard University)
Speaker's URL: https://people.math.harvard.edu/~alpoge/
Abstract: I will give a finite-time algorithm that, on input (g,K,S) with g > 0, K a totally real number field of odd degree, and S a finite set of places of K, outputs the finitely many g-dimensional abelian varieties A/K which are of GL_2-type over K and have good reduction outside S.
The point of this is to effectively compute the S-integral K-points on a Hilbert modular variety, and the point of that is to be able to compute all K-rational points on complete curves inside such varieties.
This gives effective height bounds for rational points on infinitely many curves and (for each curve) over infinitely many number fields. For example one gets effective height points for odd-degree totally real points on x^6 + 4y^3 = 1, by using the hypergeometric family associated to the arithmetic triangle group \Delta(3,6,6).
Zoom (email organizers for link)
OSU ASC Drupal 8
ascwebservices@osu.edu
America/New_York
public
Date Range
Add to Calendar
2021-11-29 16:15:00
2021-11-29 17:15:00
Effective height bounds for odd-degree totally real points on some curves
Title: Effective height bounds for odd-degree totally real points on some curves.
Speaker: Levent Alpoge (Harvard University)
Speaker's URL: https://people.math.harvard.edu/~alpoge/
Abstract: I will give a finite-time algorithm that, on input (g,K,S) with g > 0, K a totally real number field of odd degree, and S a finite set of places of K, outputs the finitely many g-dimensional abelian varieties A/K which are of GL_2-type over K and have good reduction outside S.
The point of this is to effectively compute the S-integral K-points on a Hilbert modular variety, and the point of that is to be able to compute all K-rational points on complete curves inside such varieties.
This gives effective height bounds for rational points on infinitely many curves and (for each curve) over infinitely many number fields. For example one gets effective height points for odd-degree totally real points on x^6 + 4y^3 = 1, by using the hypergeometric family associated to the arithmetic triangle group \Delta(3,6,6).
Zoom (email organizers for link)
Department of Mathematics
math@osu.edu
America/New_York
public