Personal website of Philipp Habegger

Contact

Departement Mathematik und Informatik
Fachbereich Mathematik
Spiegelgasse 1
4051 Basel
Switzerland
Email: (first name)(dot)(last name)(at symbol)unibas(.)ch
MR Author ID: 774657
Official University of Basel site

Research Interests

Number Theory, Diophantine Geometry, Arithmetic of abelian varieties, equidistribution in connected with diophantine problems, effectivity questions

Preprints

Publications

  1. "Uniform bound for the number of rational points on a pencil of curves" joint with V. Dimitrov and Z. Gao, to appear in Int. Math. Res. Not. [arXiv:1904.07268]

  2. "Heights in families of abelian varieties and the Geometric Bogomolov Conjecture" joint with Z. Gao, Ann. of Math. (2) 189 (2019), no. 2, 527-604. [arXiv:1801.05762]

  3. "No singular modulus is a unit" joint with Yu. Bilu and L. Kühne, to appear in Int. Math. Res. Not. [arXiv:1805.07167, link to scripts on GitHub]

  4. "Distribution of integral division points on the algebraic torus" joint with S. Ih, Trans. Amer. Math. Soc 371 (2019), no. 1, 357-386

  5. "Diophantine Approximations on Definable Sets" Selecta Math. (N.S.) 24 (2018), no. 2, 1633-1675 [arXiv:1608.04547]

  6. "The Norm of Gaussian Periods" Q. J. Math. 69 (2018), no. 1, 153-182 [arXiv:1611.07287]

  7. "Bad reduction of genus 2 curves with CM jacobian varieties" joint with F. Pazuki, Compos. Math. 153 (2017), no. 12, 2534-2576 [arXiv:1506.02485]

  8. "Effective Height Bounds on the Algebraic Torus", Around the Zilber-Pink conjecture/Autour de la conjecture de Zilber-Pink, 167-242, Panor. Synthèse, 52, Soc. Math. France, Paris, 2017 [arXiv:1201.3255]

  9. "Quasi-equivalence of heights and Runge's Theorem", Number Theory -- Diophantine problems, uniform distribution and applications, 257-280, Springer, Cham, 2017 [arXiv:1608.04206]

  10. "Six unlikely intersection problems in search of effectivity" joint with G. Jones and D. Masser, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 3, 447-477 [arXiv:1509.06573]

  11. "Teichmüller curves in genus three and just likely intersections in ${\bf G}_m^n\times{\bf G}_a^n$" joint with M. Bainbridge and M. Möller, Publ. Math. Inst. Hautes Études Sci. 124 (2016), 1-98 [arXiv:1410.6835]

  12. "O-minimality and certain atypical intersections" joint with J. Pila, Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 4, 813-858 [arXiv:1409.0771]

  13. "Singular Moduli that are Algebraic Units", Algebra Number Theory 9 (2015), no. 7, 1515-1524 [arXiv:1402.1632]

  14. "Small Points and Free Abelian Groups" joint with R. Grizzard and L. Pottmeyer, Int. Math. Res. Not. IMRN 2015, no. 20, 10657-10679 [arXiv:1408.4915]

  15. "A Note on Divisible Points of Curves" joint with M. Bays, Trans. Amer. Math. Soc. 367 (2015), no. 2, 1313-1328 [arXiv:1301.5674]

  16. "The Tate-Voloch Conjecture in a Power of a Modular Curve", Int. Math. Res. Not. IMRN 2014, no. 12, 3303-3339 [arXiv:1210.3299]

  17. "Small Height and Infinite Non-Abelian Extensions", Duke Math. J. 162 no. 11 (2013), 1895-2076 [arXiv:1109.5859]

  18. "Special Points on Fibered Powers of Elliptic Surfaces", J. Reine Angew. Math., 685 (2013), 143-179 [arXiv:1110.1908]

  19. "Torsion Points on Elliptic Curves in Weierstrass Form", Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XII (2013), 687-715 [arXiv:1105.4435]

  20. "Some Unlikely Intersections Beyond André-Oort" joint with J. Pila, Compositio Math. 148 (2012), 1 - 27

  21. "A Note on Maurin's Theorem" joint with E. Bombieri, D. Masser, and U. Zannier, Rend. Lincei Math. App. 21 (2010), 251 - 260

  22. "Weakly Bounded Height on Modular Curves", Acta Math. Vietnam. 35 (2010), no. 1. 43-70 [offical PDF]

  23. "Multiplicative dependence and isolation II", J. Lond. Math. Soc. (2) 80 (2009), no. 2, 495-513

  24. "Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension", Invent. Math. 176 (2009), no. 2, 405-447

  25. "A Bogomolov property modulo algebraic subgroups", Soc. Math. France 137 (2009), no. 1, 93-125

  26. "On the Bounded Height Conjecture", Int. Math. Res. Not. IMRN (2009); doi: 10.1093/imrn/rnn149

  27. "Intersecting subvarieties of ${\mathbf G}_m^n$ with algebraic subgroups" , Math. Ann. 342 (2) (2008), 449-466

  28. "Multiplicative dependence and isolation I", Diophantine Geometry, Scuola Normale Superiore, Serie CRM, Vol. 4 (2007)

  29. "The equation $x+y=\alpha$ in multiplicatively dependent unknowns" , Acta Arith. 119 (2005), 349-372

Book chapters

  1. "The Manin-Mumford conjecture, an elliptic curve, its torsion points and their Galois orbits", O-Minimality and Diophantine Geometry (G.O. Jones and A.J. Wilkie, eds.), Cambridge University Press, 2015, London Mathematical Society Lecture Note Series 421.

Updated on January 29, 2020