Prof. Dr. Gerd Faltings

E-mail: faltings(at)
Phone: +49 228 402 229
Location: Max Planck Institute for Mathematics
Institute: Max Planck Institute for Mathematics
Research Areas: Former Research Area E (Leader)
Research Area DE
Former Research Area D
Former Research Area F
Date of birth: 28.Jul 1954
Mathscinet-Number: 65080

Academic Career


PhD, University of Münster

1978 - 1979

Visitor, Harvard University, Cambridge, MA, USA

1979 - 1982

Assistant Professor, University of Münster


Habilitation, University of Münster

1982 - 1984

Professor, University of Wuppertal

1985 - 1994

Professor, Princeton University, NJ, USA

Since 1994

Scientific Member, Max Planck Institute for Mathematics, Bonn

Since 1995

Director, Max Planck Institute for Mathematics, Bonn

Research Profile

Diophantine equations

Arakelov theory

Abelian varieties

Moduli spaces of vectorbundles

p-adic Hodge theory

Research Projects and Activities

I do research on whatever I find interesting.

DFG Cluster of Excellence “Hausdorff Center for Mathematics”,
Principal Investigator and member of the Board of Directors

Contribution to Research Areas

Former Research Area D
I have found a crystalline version of nonabelian p-adic Hodge theory for ‘small’ representations. Motivic cohomology and Diophantine equations: Kim has introduced a new method into Diophantine approximation. The paper [1] constructs a motivic logarithm for arbitrary curves. An open question is the construction of such an object in algebraic K-theory, as well as a good definition of torsors over it.
Former Research Area E
Using the Hitchin fibration, the dimension of global sections for line-bundles of central charge one on moduli spaces of G-bundles has been computed in [2]. In [3], I determined the image of the Rapoport-Zink period map in the case of GL(n), confirming conjectures of Hartl and Rapoport-Zink.
Research Area DE
I extended the definition of the category MF to the semistable case. As an application I could construct semistable models for certain Shimura-varieties defined by Spin-groups with level-structure, see [4]. I also obtained estimates for the norms of Weierstrass-sections on curves.

Selected Publications

[1] Gerd Faltings
Mathematics around Kim's new proof of Siegel's theorem
Diophantine geometry
of CRM Series : 173--188
Publisher: Ed. Norm., Pisa
[2] Gerd Faltings
Theta functions on moduli spaces of G-bundles
J. Algebraic Geom. , 18: (2): 309--369
DOI: 10.1090/S1056-3911-08-00499-2
[3] Gerd Faltings
Coverings of p-adic period domains
J. Reine Angew. Math. , 643: : 111--139
DOI: 10.1515/CRELLE.2010.046
[4] G. Faltings
The category ℳℱ in the semistable case
Izv. Ross. Akad. Nauk Ser. Mat. , 80: (5): 41--60
DOI: 10.4213/im8490
[5] Gerd Faltings
Algebraic loop groups and moduli spaces of bundles
J. Eur. Math. Soc. (JEMS) , 5: (1): 41--68
DOI: 10.1007/s10097-002-0045-x
[6] Gerd Faltings
Almost étale extensions
Cohomologies p-adiques et applications arithmétiques, II
Astérisque (279): 185--270
[7] Gerd Faltings
A relation between two moduli spaces studied by V. G. Drinfeld
Algebraic number theory and algebraic geometry
of Contemp. Math. : 115--129
Publisher: Amer. Math. Soc., Providence, RI
DOI: 10.1090/conm/300/05145
[8] Gerd Faltings
A proof for the Verlinde formula
J. Algebraic Geom.
, 3: (2): 347--374
[9] Gerd Faltings
Stable G-bundles and projective connections
J. Algebraic Geom. , 2: (3): 507--568
[10] Gerd Faltings
Diophantine approximation on abelian varieties
Ann. of Math. (2) , 133: (3): 549--576
DOI: 10.2307/2944319
[11] Gerd Faltings, Ching-Li Chai
Degeneration of abelian varieties
With an appendix by David Mumford
of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] : xii+316
Publisher: Springer-Verlag, Berlin
ISBN: 3-540-52015-5
DOI: 10.1007/978-3-662-02632-8
[12] Gerd Faltings
Calculus on arithmetic surfaces
Ann. of Math. (2) , 119: (2): 387--424
DOI: 10.2307/2007043

Publication List


• Compositio Mathematica (Associate Editor)
• Journal of Algebraic Geometry (Editorial Board)



Dannie Heinemann Prize


Fields Medal


Guggenheim Fellowship


Member of the Göttingen Academy of Sciences and Humanities


Member of the German National Academy of Sciences Leopoldina


Leibniz Prize


Member of the Berlin-Brandenburg Academy of Sciences and Humanities


Member of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts


Karl Georg Christian von Staudt Prize


Bundesverdienstkreuz I. Klasse (Officer's Cross of the Order of Merit of the Federal Republic of Germany)


Heinz Gumin Prize for Mathematics


Honorary Doctorate, University of Münster


King Faisal International Prize


Member of the Academia Europaea


Shaw Prize


Foreign Associate of the Royal Society


Cantor medal of the German Mathematical Society (Deutsche Mathematiker-Vereinigung, DMV)

Selected Invited Lectures


International Congress of Mathematicians, plenary address, Berkeley, CA, USA


International Congress of Mathematicians, invited talk, Zürich, Switzerland


Heidelberg Laureate Forum


Harald Bohr Lecture, Copenhagen, Denmark


Chinese Academy of Sciences, Peking, China

Selected PhD students

Michael Larsen (1988): “Unitary Groups and L-Adic Representations”,
now Professor, Indiana University, IN, USA

Wieslawa Niziol (1991): “On A Cohomological Functor Associated To Crystalline Representations”,
now Directrice de recherche, CNRS, UMPA, École Normale Supérieure de Lyon, France

Shinichi Mochizuki (1992): “The Geometry of the Compactification of the Hurwitz Scheme”,
now Professor, Kyoto University, Japan

Tyler Jarvis (1994): “Compactification Of The Moduli Space Of Generalized Spin Curves”,
now Professor, Brigham Young University, UT, USA

Christian Liedtke (2004): “On Fundamental Groups of Galois Closures of Generic Projections”,
now Professor, TU Munich

Majid Hadian (2010): “Motivic Fundamental Groups and Integral Points”,
now Scott-Russell-Johnson Research Assistant Professor, California Institute of Technology, Pasadena, CA, USA

Supervised Theses

  • PhD theses: 1, currently 1
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