Philip Dittmann
I am a researcher at the Institut für Algebra working in the research group of Prof. Arno Fehm. I am interested in various problems related to field theory, with motivation and techniques coming from number theory, model theory, and algebraic geometry. In particular this includes definability questions over global fields and finitely generated fields, with a view towards variants of Hilbert's Tenth Problem.
Papers and preprints
- Universally defining subrings in function fields (with Nicolas Daans) - manuscript
- On the existential theory of the completions of a global field (with Arno Fehm) - manuscript
- Uniform existential definitions of valuations in function fields in one variable (with Karim Johannes Becher, Nicolas Daans) - manuscript
- Characterising local fields of positive characteristic by Galois theory and the Brauer group - manuscript
- Ax-Kochen-Ershov principles for finitely ramified henselian fields (with Sylvy Anscombe, Franziska Jahnke) - manuscript
- Two examples concerning existential undecidability in fields - to appear in the Journal of Symbolic Logic
- When is the étale open topology a field topology? (with Erik Walsberg, Jinhe Ye) - to appear in Israel Journal of Mathematics
- Definable valuations on ordered fields (with Franziska Jahnke, Lothar Sebastian Krapp, Salma Kuhlmann) - Model Theory 2(1):101-120, 2023
- Axiomatizing the existential theory of F_p((t)) (with Sylvy Anscombe, Arno Fehm) - Algebra & Number Theory 17(11):2013-2032, 2023
- Appendix to Galois groups of large fields with simple theory by Anand Pillay and Erik Walsberg - Model Theory 2(2):357-380, 2023
- Existential rank and essential dimension of diophantine sets (with Nicolas Daans, Arno Fehm) - manuscript
- Odoni's conjecture on arboreal Galois representations is false (with Borys Kadets) - Proceedings of the American Mathematical Society 150(8):3335-3343, 2022
- Characterizing finitely generated fields by a single field axiom (with Florian Pop) - Annals of Mathematics 198(3):1203-1227, 2023
- Non-definability of rings of integers in most algebraic fields (with Arno Fehm) - Notre Dame Journal of Formal Logic 62(3):589-592, 2021
- A class of fields with a restricted model completeness property (with Dion Leijnse) - Journal of Symbolic Logic 86(2):701-708, 2021
- Denseness results in the theory of algebraic fields (with Sylvy Anscombe, Arno Fehm) - Annals of Pure and Applied Logic 172(8), 2021
- The dimension growth conjecture, polynomial in the degree and without logarithmic factors (with Wouter Castryck, Raf Cluckers, Kien Huu Nguyen) - Algebra & Number Theory 14(4):2261-2294, 2020 (see the addenda file on RC's homepage for minor corrections, affecting none of the main theorems of the paper)
- A p-adic analogue of Siegel's Theorem on sums of squares (with Sylvy Anscombe, Arno Fehm) - Mathematische Nachrichten 293(8):1434-1451, 2020
- Approximation theorems for spaces of localities (with Sylvy Anscombe, Arno Fehm) - Mathematische Zeitschrift 296(3):1471-1499, 2020
- Irreducibility of Polynomials over Global Fields is Diophantine - Compositio Math. 154 (4):761-772, 2018
I wrote my doctoral thesis A Model-Theoretic Approach to the Arithmetic of Global Fields at the University of Oxford under the supervision of Jochen Koenigsmann.
Contact
+49 351 463-33908
Zellescher Weg 12-14
Willersbau Zi. C 114
TU Dresden
Fachrichtung Mathematik
Institut für Algebra
01062 Dresden