# 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

• "Uniformity in Mordell-Lang for curves" joint with V. Dimitrov and Z. Gao [arXiv:2001.10276]

• "Galois orbits of torsion points near atoral sets" joint with V. Dimitrov [arXiv:1909.06051]

• "The geometric Bogomolov conjecture" joint with S. Cantat, Z. Gao, J. Xie [arXiv:1801.05762]

## 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