publications: preprints


  1. Infinite series of quaternionic 1-vertex cube complexes, the doubling construction, and explicit cubical Ramanujan complexes
    with Nithi Rungtanapirom and Alina Vdovina
    preprint, Frankfurt-Newcastle, August 2018, arXiv:1808.03290
    to appear in International Journal of Algebra and Computation.

publications: journals


  1. Cubic twin prime polynomials are counted by modular form
    with Lior Bary-Soroker
    preprint, Frankfurt-Tel Aviv, November 2017, arXiv:1711.05564
    to appear in Canadian Journal of Mathematics.
    DOI: 10.4153/CJM-2018-018-9
  2. Simply transitive quaternionic lattices of rank 2 over Fq(t) and a non-classical fake quadric
    with Alina Vdovina
    Math. Proc. of the Cambridge Philosophical Society 163 (2017), no. 3, 453-498.
    DOI: 10.1017/S0305004117000056
  3. Arithmetic in the fundamental group of a p-adic curve - On the p-adic section conjecture for curves -
    with Florian Pop
    Journal für die Reine und Angewandte Mathematik 725 (2017), 1--40.
    DOI: 10.1515/crelle-2014-0077
  4. Anabelian geometry with étale homotopy types
    with Alexander Schmidt
    Annals of Mathematics 184 (2016), no. 3, 817-868.
    DOI: 10.4007/annals.2016.184.3.5
  5. Series of p-groups with Beauville structure
    with Alina Vdovina
    Monatshefte der Mathematik 181 (2016), no. 1, 177-186.
    DOI: 10.1007/s00605-015-0805-9
  6. Categories of abelian varieties over finite fields I. Abelian varieties over Fp
    with Tommaso Centeleghe
    Algebra & Number Theory 9 (2015), no. 1, 225-265.
    DOI: 10.2140/ant.2015.9.225
  7. On the birational section conjecture with local conditions
    Inventiones mathematicae 199 (2015), no. 1, 239-265.
    DOI: 10.1007/s00222-014-0514-3
  8. Galois sections for abelian varieties over number fields
    with Mirela Çiperiani
    Journal de Théorie des Nombres de Bordeaux 27 (2015), no. 1, 47-52.
    Journal de Théorie des Nombres de Bordeaux
  9. Weil-Châtelet divisible elements in Tate-Shafarevich groups II:
    On a question of Cassels
    with Mirela Çiperiani
    Journal für die Reine und Angewandte Mathematik 700 (2015), 175-207.
    DOI: 10.1515/crelle-2013-0013
  10. Lifting Galois sections along torsors
    with Niels Borne and Michel Emsalem
    Mathematische Nachrichten 288 (2015), no. 17-18, 1939-1951.
    DOI: 10.1002/mana.201400251
  11. Étale contractible varieties in positive characteristic
    with Armin Holschbach and Johannes Schmidt
    Algebra & Number Theory 8 (2014), no. 4, 1037-1044.
    DOI: 10.2140/ant.2014.8.1037
  12. Weil-Châtelet divisible elements in Tate-Shafarevich groups I:
    The Bashmakov problem for elliptic curves over Q
    with Mirela Çiperiani
    Compositio Mathematica 149 (2013), no. 5, 729-753.
    DOI: 10.1112/S0010437X12000747
  13. Birational p-adic Galois sections in higher dimensions
    Israel Journal of Mathematics 198 (2013), no. 1, 49-61.
    DOI: 10.1007/s11856-012-0189-7
  14. The Brauer-Manin obstruction for sections of the fundamental group
    Journal of Pure and Applied Algebra 215 (2011), no. 6, 1371-1397.
    DOI: 10.1016/j.jpaa.2010.08.017
  15. On the period-index problem in light of the section conjecture
    American Journal of Mathematics 132 (2010), no. 1, 157-180.
    DOI: 10.1353/ajm.0.0092
  16. Trading degree for dimension in the section conjecture: The non-abelian Shapiro Lemma
    Mathematical Journal of Okayama University 52 (2010), 29-43.
    Mathematical Journal of Okayama University
    See also the following harmless correction.
  17. A general Seifert-Van Kampen theorem for algebraic fundamental groups
    Publications of RIMS 42 (2006), no. 3, 763-786.
    DOI: 10.2977/prims/1166642159
  18. A monodromy criterion for extending curves
    International Mathematics Research Notices (2005), no. 29, 1787-1802.
    DOI: 10.1155/IMRN.2005.1787
  19. A logarithmic view towards semistable reduction
    Journal of Algebraic Geometry 14 (2005), no. 1, 119-136.
    DOI: 10.1090/S1056-3911-04-00388-1
  20. Affine Anabelian Curves in Positive Characteristic
    Compositio Mathematica 134 (2002), no. 1, 75-85.
    DOI: 10.1023/A:1020290619656

publications: proceedings


  1. Anabelian geometry with étale homotopy types II
    to appear in: Arithmetic Geometry and Symmetries around Galois and Fundamental Groups, Oberwolfach report 17 (2018), no. xx, yy-zz.
  2. On Galois sections for hyperbolic p-adic curves
    in: The Arithmetic of Fields, Oberwolfach report 10 (2013), no. 2, 1799-1804.
  3. Birational Galois sections with local conditions for hyperbolic curves
    in: Arithmetic Geometry, Oberwolfach report 9 (2012), no. 3, 2339-2342.
  4. On cuspidal sections of algebraic fundamental groups
    in: "Galois-Teichmüller Theory and Arithmetic Geometry", Proceedings for a Conferences in Kyoto (October 2010), H. Nakamura, F. Pop, L. Schneps, A. Tamagawa eds., Advanced Studies in Pure Mathematics 63, 2012, 519-563.
  5. Descent obstruction and fundamental exact sequence
    with David Harari
    in: J. Stix (editor): The Arithmetic of Fundamental Groups - PIA 2010
    Contributions in Mathematical and Computational Sciences, Vol. 2, Springer-Verlag Berlin Heidelberg, 2012.
  6. Nonabelian examples for the section conjecture in anabelian geometry
    in: Algebraic Number Theory, Oberwolfach report 6 (2009), no. 2, 1720-1722.
  7. On the period-index problem in light of the section conjecture
    in: The Arithmetic of Fields, Oberwolfach report 6 (2009), no. 1, 293-295.
  8. On the geometry of higher dimensional anabelian varieties
    in: Arithmetic and Differential Galois Groups, Oberwolfach report 4 (2007), no. 2, 1501-1504.
  9. Anabelian properties of the moduli spaces of smooth projective curves
    in: The Arithmetic of Fields, Oberwolfach report 3 (2006), no. 1, 364-367.

publications: thesis


  1. Evidence for the section conjecture in the theory of arithmetic fundamental groups
    Habilitationsschrift, School of Mathematics and Computer Science at the Ruprecht-Karls-Universität Heidelberg, January 2011, x+190 pages, to appear as
    Rational Points and Arithmetic of Fundamental Groups
    Evidence for the Section Conjecture
    Springer Lecture Notes in Mathematics 2054, xx+pp.249, Springer, 2013.
    Erratum for curves that are space filling in their jacobian.
  2. Projective Anabelian Curves in Positive Characteristic and Descent Theory for Log-Etale Covers
    Dissertation, 2002, Bonn, Bonner Mathematische Schriften, 354 (2002)
    with a short version in german (Oktober 2004).
    The thesis was awarded the Felix-Hausdorff-Gedächtnispreis of the academic year 2002/2003 by the department of mathematics of the Rheinischen Friedrich-Wilhelms-Universität Bonn.
  3. Affine anabelsche Kurven in positiver Charakteristik
    diploma thesis, Bonn, 2000.

Books


  1. Rational Points and Arithmetic of Fundamental Groups
    Evidence for the Section Conjecture

    Springer Lecture Notes in Mathematics 2054, 2013.
    Erratum for curves that are space filling in their jacobian.

  2. The Arithmetic of Fundamental Groups - PIA 2010

    editor J. Stix, Contributions in Mathematical and Computational Sciences, Vol. 2, Springer-Verlag Berlin Heidelberg, 2012.