- Big semistable vector bundles
- Preprint, 2002. This preprint formulates a conjecture on big semistable vector bundles on projective varieties. It also proves the conjecture for vector bundles over curves. Work supported by NSF grant DMS-0200892.
- A quantitative proof of Roth's theorem with moving targets
- Preprint, 1995. This is available as a
`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. This paper was formerly titled**Roth's theorem with moving targets**. - On McQuillan's "tautological inequality" and the Weyl-Ahlfors theory of associated curves
- Preprint, 2007; arXiv:0706.3044.
- Nagata's embedding theorem
- Preprint, 2007; arXiv:0706.1907.
- Transplanting Faltings' garden
- Preprint, 2009; arXiv:0901.2106.

- A higher dimensional Mordell conjecture
- In:
*Arithmetic Geometry*, ed. by G. Cornell and J. H. Silverman, Springer-Verlag, New York, 1986, pp. 341–353. MR 89b:14029 (whole collection); Zbl. 605.14019. - A diophantine conjecture over
*Q* - In:
*Seminaire de Theorie des Nombres, Paris 1984–85*, ed. by Catherine Goldstein, Progress in Mathematics 63, Birkhauser, Boston-Basel-Stuttgart, 1986, pp. 241–250. MR 88h:11045; Zbl. 601.14016. - Examples of some
-admissible groups (joint with W. Feit)*Q* *J. of Number Theory***26**(1987), pp. 210–226. Unfortunately, this paper contains a serious error which invalidates the main result. MR 88g:12006; Zbl. 619.12007.- Diophantine approximations and value distribution theory
- Lecture Notes in Mathematics 1239, Springer-Verlag, New York, 1987.
132+x pp.
MR 91k:11049; Zbl. 609.14011.

List of errata and addenda: dvi, pdf.

A scanned copy of the book is now available from springerlink (access restricted, except for front matter and back matter). - A refinement of Schmidt's subspace theorem
*The American Journal of Mathematics*,**111**(1989), pp. 489–518. MR 90f:11054; Zbl. 662.14002.- Dyson's lemma for products of two curves of arbitrary genus
*Invent. Math.***98**(1989), pp. 107–113. MR 90k:11075; Zbl. 666.10024.- Mordell's conjecture over function fields
*Invent. Math.***98**(1989), pp. 115–138. MR 90k:11076; Zbl. 662.14019.- Diophantine inequalities and Arakelov theory
- In: S. Lang,
*Introduction to Arakelov Theory*, Springer, 1988, pp. 155–178. MR 89m:11059 (whole book); Zbl. 667.14001 (whole book). - Arithmetic discriminants and quadratic points on curves
- In: G. van der Geer, F. Oort, and J. H. M. Steenbrink, eds.,
*Arithmetic algebraic geometry, Texel 1989*, Birkhauser, Boston, 1991, pp. 359–376. MR 92j:11059; Zbl. 749.14018. - On algebraic points on curves
*Comp. Math.***78**(1991), pp. 29–36. MR 93b:11080; Zbl. 731.14015.- Siegel's theorem in the compact case
*Ann. Math.***133**(1991), pp. 509–548. MR 93d:11065; Zbl. 774.14019.- Recent work on Nevanlinna theory and Diophantine approximation
- In: W. Stoll, ed.,
*Proceedings Symposium on Value Theory in Several Complex Variables, Notre Dame, Indiana, April, 1990*, University of Notre Dame Press, Notre Dame, 1992, pp. 107–113. MR 95c:11095; Zbl. 871.11043. - Arithmetic and hyperbolic geometry
- In:
*Proceedings of the International Congress of Mathematicians, Kyoto, Japan, August 1990*, Springer, Tokyo, 1991, pp. 757–765. MR 93e:11080; Zbl. 745.14007. - A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing
*Journal of the AMS***5**(1992), pp. 763–804. MR 94a:11093; Zbl. 778.11037.- Arithmetic of Subvarieties of Abelian and Semiabelian Varieties
- In:
*Advances in Number Theory (Proceedings of the Canadian Number Theory Association, Queens University, Kingston, Ontario, August, 1991)*, Fernando Q. Gouvea and Noriko Yui, eds., Clarendon Press, Oxford, 1993, pp. 233–238. MR 97a:11101; Zbl. 790.11048. - Applications of arithmetic algebraic geometry to diophantine approximations
- In:
*Arithmetic Algebraic Geometry, Trento, 1991*, Lecture Notes in Mathematics 1553, Springer-Verlag, Heidelberg, 1993, pp. 164–208. This is available as a`TeX`file, which in turn requires a special macro file`PVmacs.sln`. MR 96c:11067; Zbl. 846.14009 (individual article) and 780.00022 (whole book). - Roth's theorem with moving targets
*International Mathematics Research Notices***1996**(1996), pp. 109–114. An earlier version of this paper had the title**Roth's theorem with moving targets – the sequel**. MR 96k:11087; Zbl. 877.11041.- Integral points on subvarieties of semiabelian varieties, I
*Inventiones Mathematicae***126**(1996), pp. 133–181. MR 98a:14034; Zbl. 1011.11040.- Schmidt's Subspace Theorem with moving targets (joint with Min Ru)
*Inventiones Mathematicae***127**(1997), pp. 51–65. MR 97g:11076; Zbl. 1013.11044.- On Cartan's Theorem and Cartan's Conjecture
*The American Journal of Mathematics***119**(1997), pp. 1–17. MR 97m:32041; Zbl. 877.11040.- A more general abc conjecture
*International Mathematics Research Notices***1998**(1998), pp. 1103–1116. This is available as a`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. MR 99k:11096; Zbl. 923.11059.- Integral points on subvarieties of semiabelian varieties, II
*The American Journal of Mathematics***121**(1999), pp. 283–313. This is available as a`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. MR 2000d:11074; Zbl. 1018.11027.- Nevanlinna theory and diophantine approximation
- In:
*Several complex variables*(Math. Sci. Res. Inst. Publ. #37), Michael Schneider and Yum-Tong Siu, eds., Cambridge U. Press, New York, 1999, pp. 535–564. This is available as a`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. MR 2001j:11072; Zbl. 960.32013. - On the abc conjecture and diophantine approximation by rational points
*The American Journal of Mathematics***122**(2000), pp. 843–872. This is available as a`TeX`file, which also requires a`MetaPost`file, in addition to the generic macro file`PVmacs.tex`. MR 2001i:11094; Zbl. 1037.11052.- Diagonal quadratic forms and Hilbert's tenth problem
- In:
*Hilbert's tenth problem: relations with arithmetic and algebraic geometry (Ghent, Belgium, 1999)*(Contemporary Mathematics #270), Jan Denef, Leonard Lipshitz, Thanases Pheidas, Jan Van Geel, eds., American Mathematical Society, Providence, R.I., 2000, pp. 261–274. This is available as a`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. MR 2001k:11260; Zbl. 0995.11070. - Correction to "On the abc conjecture and diophantine approximation by rational points"
*The American Journal of Mathematics***123**(2001), pp. 383–384. This is available as a`TeX`file, which in turn requires the generic macro file`PVmacs.tex`. MR 2002d:11095; Zbl. 1037.11053.- Arithmetic jet spaces
- In:
*Proceedings of Hayama Symposium on Several Complex Variables 2004, December 18–21*, ed. by Y. Nishimura, et al., Shonan Village, Hayama, Japan, 2005, pp. 134–143. - On the Nochka-Chen-Ru-Wong proof of Cartan's Conjecture
*Journal of Number Theory***125**(2007), pp. 229–234. Gives a mild shortening of the construction of weights associated to hyperplanes in Nochka's proof of the Cartan conjecture on holomorphic curves approximating hyperplanes in*n*-subgeneral position. Work supported by NSF grants DMS-9304899, DMS-0200892, and DMS-0500512.- Jets via Hasse-Schmidt derivations
- In:
*Diophantine Geometry, Proceedings*, U. Zannier (ed.), Edizioni della Normale, Pisa, 2007, pp. 335–361. arXiv:math.AG/0407113. This note gives an expository introduction to the theory of jet spaces on arbitrary schemes, defined using Hasse-Schmidt derivations. It was written as a part of the seminar on motivic integration taking place at MSRI. Work supported by NSF grant DMS-0200892. - Diophantine approximation and Nevanlinna theory
- In:
*Arithmetic Geometry, Cetraro, Italy 2007,*Lecture Notes in Mathematics 2009, Springer-Verlag, Berlin Heidelberg, 2011, pp. 111–230. - Multiplier ideal sheaves, Nevanlinna theory, and diophantine approximation
- In:
*Number theory, analysis and geometry: In memory of Serge Lang,*ed. by Dorian Goldfeld, Jay Jorgenson, Peter Jones, Dinakar Ramakrishnan, Kenneth A. Ribet, and John Tate, Springer, New York, 2012, pp. 647–658. arXiv:0709.3322. - A Lang exceptional set for integral points
- In:
*Geometry and analysis on manifolds: In memory of Professor Shoshichi Kobayashi,*ed. by Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, and Alan Weinstein, Springer International, Cham Heidelberg New York Dordrecht London, 2015, pp. 177–207. - The Thue-Siegel method in diophantine geometry
- In:
*Rational points, rational curves, and entire holomorphic curves on projective varieties,*ed. by Carlo Gasbarri, Steven Lu, Mike Roth, and Yuri Tschinkel, American Mathematical Society, Providence, RI, 2015, pp. 109–129. - A birational Nevanlinna constant and its consequences (joint with Min Ru)
*Amer. J. Math.***142**(2020), pp. 957–991, https://muse.jhu.edu/article/755114/pdf- Roth's Theorem over arithmetic function fields
*Algebra Number Theory*15 (8) (2021), 1943–2017. arXiv:1806.10737.- An Evertse–Ferretti Nevanlinna constant and its consequences (joint with Min Ru)
*Monatsh. Math.*, 196 (2) (2021), pp. 305–334, https://doi.org/10.1007/s00605-021-01600-1, http://link.springer.com/article/10.1007/s00605-021-01600-1.- Birational Nevanlinna constants, beta constants, and diophantine approximation to closed subschemes
- Submitted Sept. 2020, arXiv:2008.00405.

Paul Vojta / vojta@math.berkeley.edu