Valentijn Karemaker's homepage

Research

My research interests lie in the fields of arithmetic geometry and algebraic number theory. Currently I am thinking about arithmetic properties of (supersingular) varieties and Drinfeld modules over finite fields, (local-global principles for) rational points on varieties, anabelian geometry, and Galois representations.
Previously I also worked on (dynamical) Belyi maps, adelic algebraic groups, automorphic representations, and Galois representations attached to abelian varieties.

Keywords: Arithmetic of varieties over finite fields, local-global principles, rational points, Galois representations, algebraic groups, anabelian geometry, arithmetic curves, zeta functions, Neukirch-Uchida theory, abelian varieties.

Publications

8. A comparison between obstructions to local-global principles over semiglobal fields (submitted, 2019, ArXiV), with D. Harbater, J. Hartmann, and F. Pop.

7. Dynamical Belyi maps and arboreal Galois groups (submitted, 2018, ArXiV), with I. Bouw and O. Ejder.

6. Fully maximal and fully minimal abelian varieties (Journal of Pure and Applied Algebra, 223(7), 3031-3056, 2019, ArXiV), with R. Pries.

5. Dynamical Belyi maps (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, 2016, ArXiV).

3. Large Galois images for Jacobian varieties of genus 3 curves (Acta Arithmetica, 174(4), 339-366, 2016, 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, 2017, pdf), with G. Cornelissen.

1. Galois representations and symplectic Galois groups over Q (Women in Numbers Europe, Association for Women in Mathematics Series, Springer, 2015, 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

Thinking Positive: Arithmetic Geometry in Characteristic p, AMS Notices article (available here), with R. Bell, J. Hartmann, P. Srinivasan, and I. Vogt.

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