Valentijn Karemaker's homepage

Research

My research interests lie in the fields of arithmetic geometry and algebraic number theory. Currently I am thinking about local-global principles for algebraic groups, anabelian geometry, Galois representations, supersingular (abelian) varieties, and Belyi maps.
During my PhD I also worked on adelic algebraic groups, automorphic representations, and Galois representations attached to abelian varieties.

Keywords: Algebraic groups, local-global principles, Galois representations, anabelian geometry, arithmetic curves, Neukirch-Uchida theory, abelian varieties, class field theory, (Dirichlet and Artin) L-series and zeta functions.

Publications

6. Fully maximal and fully minimal abelian varieties (submitted, ArXiV), with R. Pries.

5. Dynamical Belyi maps (to appear in Women in Numbers Europe 2, Association for Women in Mathematics Series, Springer, 2018, ArXiV), with J. Anderson, I. Bouw, O. Ejder, N. Girgin, and M. Manes.

4. Hecke algebras for GLn over local fields (Archiv der Mathematik, 107(4), 341-353, ArXiV).

3. Large Galois images for Jacobian varieties of genus 3 curves (Acta Arithmetica, 174(4), 339-366, ArXiV), with S. Arias-de-Reyna, C. Armana, M. Rebolledo, L. Thomas, and N. Vila.

2. Hecke algebra isomorphisms and adelic points on algebraic groups (Documenta Mathematica 22 (2017), 851--871, pdf), with G. Cornelissen.

1. Galois representations and symplectic Galois groups over Q (Proceedings of Women in Numbers Europe - Research Directions in Number Theory, ArXiV), with S. Arias-de-Reyna, C. Armana, M. Rebolledo, L. Thomas, and N. Vila.

PhD thesis

Hecke algebras, Galois representations, and abelian varieties (available here).
If you would like an updated version with fewer typos/mistakes, please send me an email.

Expository

Reconstruction of function fields, (notes for an anabelian geometry reading seminar talk at the Courant Institute, New York in Spring 2018).