publications: preprints
publications: journals
-
Cubic
twin prime polynomials are counted by a modular form
with Lior Bary-Soroker
Canadian Journal of Mathematics 71 (2019), no. 6,1323-1350.
DOI: 10.4153/CJM-2018-018-9 -
Infinite
series of quaternionic 1-vertex cube complexes, the doubling construction, and explicit cubical Ramanujan complexes
with Nithi Rungtanapirom and Alina Vdovina
International Journal of Algebra and Computation 29 (2019), no. 6, 951-1007.
DOI: 10.1142/S0218196719500371 -
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 -
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 -
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 -
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 -
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 -
On the birational
section conjecture with local conditions
Inventiones mathematicae 199 (2015), no. 1, 239-265.
DOI: 10.1007/s00222-014-0514-3 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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 -
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. -
A general Seifert-Van Kampen theorem for algebraic fundamental groups
Publications of RIMS 42 (2006), no. 3, 763-786.
DOI: 10.2977/prims/1166642159 -
A monodromy criterion for extending curves
International Mathematics Research Notices (2005), no. 29, 1787-1802.
DOI: 10.1155/IMRN.2005.1787 -
A
logarithmic view towards semistable reduction
Journal of Algebraic Geometry 14 (2005), no. 1, 119-136.
DOI: 10.1090/S1056-3911-04-00388-1 -
Affine
Anabelian Curves in Positive Characteristic
Compositio Mathematica 134 (2002), no. 1, 75-85.
DOI: 10.1023/A:1020290619656
publications: proceedings
-
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. -
On Galois sections for hyperbolic p-adic curves
in: The Arithmetic of Fields, Oberwolfach report 10 (2013), no. 2, 1799-1804. -
Birational Galois sections with local conditions for
hyperbolic curves
in: Arithmetic Geometry, Oberwolfach report 9 (2012), no. 3, 2339-2342. -
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. -
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. -
Nonabelian examples for the section conjecture in anabelian geometry
in: Algebraic Number Theory, Oberwolfach report 6 (2009), no. 2, 1720-1722. -
On the period-index problem in light of the section conjecture
in: The Arithmetic of Fields, Oberwolfach report 6 (2009), no. 1, 293-295. -
On the geometry of higher dimensional anabelian varieties
in: Arithmetic and Differential Galois Groups, Oberwolfach report 4 (2007), no. 2, 1501-1504. -
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
-
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. -
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. -
Affine anabelsche Kurven in
positiver Charakteristik
diploma thesis, Bonn, 2000.
Books
-
Rational Points and Arithmetic of Fundamental Groups
Evidence for the Section ConjectureSpringer Lecture Notes in Mathematics 2054, 2013.
Erratum for curves that are space filling in their jacobian. -
The
Arithmetic of Fundamental Groups - PIA 2010
editor J. Stix, Contributions in Mathematical and Computational Sciences, Vol. 2, Springer-Verlag Berlin Heidelberg, 2012.