Publications

Preprints
[-]  N. Daans, P. Dittmann and A. Fehm. Existential rank and essential dimension of diophantine sets. Manuscript, 2021. [video] [video]
[-] P. Dittmann and A. Fehm. On the existential theory of the completions of a global field. Manuscript, 2024.
[-]  S. Anscombe and A. Fehm. Universal-existential theories of fields. Manuscript, 2024.

Articles in refereed journals
[1]  A. Fehm and W.-D. Geyer. A note on defining transcendentals in function fields. The Journal of Symbolic Logic 74(4), 2009.
[2]  A. Fehm and S. Petersen. On the rank of abelian varieties over ample fields. International Journal of Number Theory 6(3), 2010.
[3]  A. Fehm. Subfields of ample fields. Rational maps and definability. Journal of Algebra 323(5), 2010.
[4]  A. Fehm. Embeddings of function fields into ample fields. manuscripta mathematica 134(3), 2011.
[5]  A. Fehm, M. Jarden and S. Petersen. Kuykian fields. Forum Mathematicum 24(5), 2012.
[6]  A. Fehm and E. Paran. Galois theory over rings of arithmetic power series. Advances in Mathematics 226(5), 2011. Erratum [6'].
[7]  A. Fehm and E. Paran. Non-ample complete valued fields. International Mathematics Research Notices 2011(18), 2011.
[8]  A. Fehm and E. Paran. Klein approximation and Hilbertian fields. Journal für die reine und angewandte Mathematik 676, 2013.
[9]  A. Fehm and S. Petersen. Hilbertianity of division fields of commutative algebraic groups. Israel Journal of Mathematics 195(1), 2013.
[10]  A. Fehm and E. Paran. Split embedding problems over the open arithmetic disc. Transactions of the American Mathematical Society 366, 2014.
[11]  A. Fehm. Elementary geometric local-global principles for fields. Annals of Pure and Applied Logic 164, 2013.
[12]  L. Bary-Soroker and A. Fehm. Random Galois extensions of Hilbertian fields. Journal de Théorie des Nombres de Bordeaux 25(1), 2013.
[13]  A. Fehm, N. Lev and E. Paran. Algebraic functions in the Wiener algebra. Communications in Algebra 42(9), 2014.
[14]  L. Bary-Soroker, A. Fehm and S. Petersen. On varieties of Hilbert type. Annales de l'Institut Fourier 64(5), 2014.
[15]  A. Fehm. Existential 0-definability of henselian valuation rings. The Journal of Symbolic Logic 80(1), 2015.
[16]  A. Fehm and F. Jahnke. On the quantifier complexity of definable canonical henselian valuations. Mathematical Logic Quarterly 61, 2015.
[17]  A. Fehm and A. Prestel. Uniform definability of henselian valuation rings in the Macintyre language. Bulletin of the London Mathematical Society 47, 2015.
[18]  L. Bary-Soroker, A. Fehm and G. Wiese. Hilbertian fields and Galois representations. Journal für die reine und angewandte Mathematik 712, 2016.
[19]  A. Fehm and F. Jahnke. Fields with almost small absolute Galois group. Israel Journal of Mathematics 214, 2016.
[20]  A. Fehm. The elementary theory of large fields of totally S-adic numbers. Journal of the Institute of Mathematics Jussieu 16, 2017.
[21]  S. Anscombe and A. Fehm. The existential theory of equicharacteristic henselian valued fields. Algebra and Number Theory 10-3, 2016.
[22]  E. Bank, L. Bary-Soroker and A. Fehm. Sums of two squares in short intervals in polynomial rings over finite fields. American Journal of Mathematics 140(4), 2018. [arXiv]
[23]  S. Anscombe and A. Fehm. Characterizing diophantine henselian valuation rings and valuation ideals. Proceedings of the London Mathematical Society 115, 2017.
[24]  L. Bary-Soroker and A. Fehm. Correlations of sums of two squares and other arithmetic functions in function fields. International Mathematics Research Notices 2019(14), 2019. [arXiv]
[25]  A. Fehm. Three counterexamples concerning the Northcott property of fields. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 29(2), 2018. [arXiv]
[26]  A. Fehm, F. Legrand and E. Paran. Embedding problems for automorphism groups of field extensions. Bulletin of the London Mathematical Society 51, 2019. [arXiv]
[27]  S. Anscombe, P. Dittmann and A. Fehm. Approximation theorems for spaces of localities. Mathematische Zeitschrift 296, 2020. [arXiv]
[28]  S. Anscombe, P. Dittmann and A. Fehm. A p-adic analogue of Siegel's theorem on sums of squares. Mathematische Nachrichten 293, 2020. [arXiv]
[29]  S. Anscombe, P. Dittmann and A. Fehm. Denseness results in the theory of algebraic fields. Annals of Pure and Applied Logic 172, 2021. [arXiv]
[30]  S. Checcoli and A. Fehm. On the Northcott property and local degrees. Proceedings of the American Mathematical Society 149, 2021. [arXiv]
[31]  A. Fehm and F. Legrand. A note on finite embedding problems with nilpotent kernel. Journal de Théorie des Nombres de Bordeaux 34(2), 2022. [arXiv]
[32]  P. Dittmann and A. Fehm. Nondefinability of rings of integers in most algebraic fields. Notre Dame Journal of Formal Logic 62(3), 2021.  [arXiv]
[33]  S. Checcoli and A. Fehm. Constructing totally p-adic numbers of small height. International Journal of Number Theory 18(3), 2022. [arXiv]
[34]  L. Bary-Soroker, A. Entin and A. Fehm. The minimal ramification problem for rational function fields over finite fields. International Mathematics Reserach Notices 2023(11), 2023. [arXiv] [video]
[35]  S. Anscombe, P. Dittmann and A. Fehm. Axiomatizing the existential theory of Fq((t)). Algebra and Number Theory 17-11, 2023. [arXiv]
[36] L. Bary-Soroker, A. Fehm and S. Petersen. Ramified covers of abelian varieties over torsion fields. Journal für die reine und angewandte Mathematik 805, 2023. [arXiv]
[37]  S. Checcoli and A. Fehm. On Widmer's criteria for the Northcott property. Proceedings of the American Mathematical Society 152, 2024. [arXiv]
[38]  L. Bary-Soroker, A. Fehm and S. Petersen. Hilbert properties under base change in small extensions. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024. [video]
[39]  S. Anscombe and A. Fehm. Interpretations of syntactic fragments of theories of fields. To appear in Israel Journal of Mathematics, 2024.

Articles in refereed conference proceedings and collections
[A]  L. Bary-Soroker and A. Fehm. Open problems in the theory of ample fields. In D. Bertrand, Ph. Boalch, J.-M. Couveignes and P. Dèbes (eds.), Geometric and differential Galois theory, Séminaires & Congrès 27, 2013.
[B]  L. Bary-Soroker and A. Fehm. On fields of totally S-adic numbers. With an appendix by Florian Pop. In A. Campillo, F.-V. Kuhlmann, B. Teissier (eds.), Valuation Theory in Interaction, EMS Series of Congress Reports, 2014.
[C]  A. Fehm and F. Jahnke. Recent progress on definability of henselian valuations. In: F. Broglia, F. Delon, M. Dickmann, D. Gondard, and V. Powers (eds.), Proceedings of the Conference on Ordered Algebraic Structures and Related Topics, Contemporary Mathematics 697, 2017.
[D]  A. Fehm, D. Haran and E. Paran. The inverse Galois problem over C(z). In: M. Jarden, T. Shaska (eds.), Abelian Varieties and Number Theory, Contemporary Mathematics 767, 2021.
[E]  A. Fehm and S. Petersen. Ranks of abelian varieties and the full Mordell-Lang conjecture in dimension one. In: M. Jarden, T. Shaska (eds.), Abelian Varieties and Number Theory, Contemporary Mathematics 767, 2021. [video]


Articles in unrefereed conference proceedings
[F]  A. Fehm. Permanence criteria for Hilbertian fields (joint work with Lior Bary-Soroker and Gabor Wiese). In M. Jarden, F. Pop (eds.), The Arithmetic of Fields. Oberwolfach Rep. 10, 2013.
[G]  A. Fehm. Existentially definable henselian valuation rings (joint work with Will Anscombe, Alexander Prestel). In Z. Chatzidakis, F.-V. Kuhlmann, J. Koenigsmann, F. Pop (eds.), Valuation theory and its applications. Oberwolfach Rep. 11, 2014.
[H]  A. Fehm. Diophantine subsets of henselian fields (joint work with Sylvy Anscombe, Philip Dittmann). In J. Koenigsmann, H. Pasten, A. Shlapentokh, X. Vidaux (eds.), Definability and decidability in number theory. Oberwolfach Rep. 13, 2016.
[J]  A. Fehm. Pseudo-algebraic fields are dense in their classical closures (joint work with Sylvy Anscombe, Philip Dittmann). In L. Bary-Soroker, F. Pop, J. Stix (eds.), Field Arithmetic. Oberwolfach Rep. 15, 2018.
[K]  A. Fehm. The minimal ramification problem over function fields (joint work with Lior Bary-Soroker, Alexei Entin).  In: B. Collas, P. Dèbes, H. Nakamura, J. Stix (eds.),
Homotopic and Geometric Galois Theory. Oberwolfach Rep. 18, 2021.

Thesis
[I]  A. Fehm. Decidability of large fields of algebraic numbers. Dissertation, Tel Aviv, 2010.

Editorial
[*] L. Bary-Soroker, D. Haran and A. Fehm. Foreword. Israel Journal of Mathematics 257(1), 2023.