Slides from recent talks and relevant references
Slides from recent talks and relevant references
Slides:
An Exploration of Sato-Tate Groups of Curves
An Exploration of Curves over Finite Fields (Math Club)
My relevant papers:
"An Exploration of Degeneracy in Abelian Varieties of Fermat Type." Experimental Mathematics, June 2024. Preprint.
"Monodromy groups and exceptional Hodge classes," (with Andrea Gallese and Davide Lombardo). 2024. Preprint.
"Nondegeneracy and Sato-Tate Distributions of Two Families of Jacobian Varieties," (with M. Emory). 2024. Preprint.
"Sato-Tate Distributions of Catalan Curves," Journal de Théorie des Nombres de Bordeaux, Volume 35 (2023), pages 87–113. Preprint.
"Sato-Tate Distributions of y^2=x^p-1 and y^2=x^{2p}-1," (with M. Emory). Journal of Algebra, Volume 597 (May 2022), pages 241 - 265. Preprint.
"Towards the Sato-Tate Groups of Trinomial Hyperelliptic Curves," (with M. Emory and A. Peyrot). International Journal of Number Theory, Volume No. 17, Issue No. 10, pp. 2175 - 2206, Year 2021. Preprint.
Other references:
(Start here! Great intro!) Sato-Tate distributions. Sutherland. Analytic Methods in Arithmetic Geometry, Contemporary Mathematics 740 (2019), 197-248.
(Another great intro!) The Sato-Tate conjecture for a Picard curve with complex multiplication (with an appendix by Francesc Fité). J.-C. Lario and A. Somoza. In Number theory related to modular curves, volume 701 of Contemp. Math., pages 151–165. 2018
(A nice textbook!) Complex Abelian Varieties. Birkenhake, Lange. Grundlehren der mathematischen Wissenschaften series (GL, volume 302). Springer-Verlag.
Sato-Tate groups of abelian threefolds. Fité, Kedlaya, Sutherland. arXiv (2021).
Sato-Tate distributions of twists of the Fermat and the Klein quartics. Fité, Lorenzo Garcia, Sutherland. Research in the Mathematical Sciences 5 (2018), article 41.
Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx. Fité, Sutherland. Frobenius distributions: Lang-Trotter and Sato-Tate conjectures, Contemporary Mathematics 663 (2016), 103-126.
Sato-Tate distributions and Galois endomorphism modules in genus 2. Fité, Kedlaya, Rotger, Sutherland. Compositio Mathematica 148 (2012), 1390-1442.
The twisting Sato-Tate group of the curve y^2 = x^8 −14x^4 + 1. S. Arora, V. Cantoral-Farfan, A. Landesman, D. Lombardo, and J. S. Morrow. Math. Z., 290(3-4):991–1022, 2018.
An algebraic Sato-Tate group and Sato-Tate conjecture. G. Banaszak and K. S. Kedlaya. Indiana Univ. Math. J., 64(1):245–274, 2015.Algebraic cycles on abelian varieties of Fermat type. Shioda. Math. Ann., 258(1):65–80 (1981/82).
Non-isogenous abelian varieties sharing the same division fields. Lombardo 2021. Preprint.