Prof. Dr. Michael Rapoport

E-mail: rapoport(at)
Phone: +49 228 73 7793
Room: N2.012
Location: Mathematics Center (Annexe)
Institute: Mathematical Institute
Research Area: Research Area A1

Academic Career


These d'Etat, University of Paris-Sud, France

1976 - 1980

Assistant Professor, HU Berlin

1982 - 1986

Professor (C3), University of Heidelberg

1986 - 1989

Professor (C3), University of Bonn

1989 - 1996

Professor (C4), University of Wuppertal

1996 - 2003

Professor (C4), University of Cologne

2003 - 2012

Professor (C4), University of Bonn

2012 - 2017

Professor (W3), University of Bonn

Since 2017


Since 2017

Visiting Professor University of Maryland

Research Profile

My aim is to use algebraic geometry to establish higher reciprocity laws, which serve as a bridge between the field of arithmetic and the theory of automorphic forms. I am interested in the theory of Shimura varieties and their local variants, in particular Rapoport-Zink spaces. I am particularly fascinated by the possibility of constructing through them interesting Galois representations, of algebraic cycles on them and of deformations. My current research focusses on the following topics. I am interested in constructing arithmetic models of Shimura varieties through the correct formulation of a moduli problem whose solution gives such a model. For Shimura varieties attached to unitary groups this naturally leads to the problem of defining a crystalline discriminant of polarized p-divisible groups. So far, I have succeeded in this in the case of even height (joint work with S. Kudla). I am also interested in understanding the structure of natural stratifications of the reduction modulo p of integral models of Shimura varieties (the Newton stratification, the Ekedahl-Oort stratification, the Kottwitz-Rapoport stratification). In joint work with X. He, I have given an axiomatic framework for studying these questions. I am also interested in the Arithmetic Fundamental Lemma conjecture of W. Zhang. This conjecture predicts the intersection number of two arithmetic cycles of half-dimension on a Rapoport-Zink space. In joint work with U. Terstiege and W. Zhang I solved this conjecture in the minuscule case. Recently, in joint work with B. Smithling and W. Zhang, I extended the conjecture to ramified cases and solved it in a number of cases of small dimension.

In my future research I want to understand better the dependence of Rapoport-Zink spaces on the underlying group theory. My recent theorem with T. Zink on the Drinfeld moduli problem of p-divisible groups deals in a special case related to {\rm GL}_2 with the effect of changing the relevant cocharacter by a central cocharacter. In future work with S. Kudla and T. Zink, I want to treat the analogous problem for the group {\rm GU}_2 and apply this to the p-adic uniformization of certain Shimura curves. I want to understand the influence of exceptional isomorphisms between orthogonal groups and unitary groups on their associated Rapoport-Zink spaces (which exist, due to recent work of B. Howard/G. Pappas and of W. Kim). Another topic I want to explore is the relation between the conjectures of S. Kudla and myself on arithmetic divisors on Rapoport-Zink spaces and the conjectures of W. Zhang on arithmetic cycles of half-dimension. I want to understand the impact of Scholze's ideas and methods on the study of integral models of Shimura varieties. I also want to return to the theory of \Phi-modules which I started with G. Pappas and make progress after the recent contributions of M. Emerton/T. Gee.

Selected Publications

[1] Michael Rapoport, Ulrich Terstiege, Wei Zhang
On the arithmetic fundamental lemma in the minuscule case
Compos. Math. , 149: (10): 1631--1666
DOI: 10.1112/S0010437X13007239
[2] Stephen Kudla, Michael Rapoport
Special cycles on unitary Shimura varieties I. Unramified local theory
Invent. Math. , 184: (3): 629--682
DOI: 10.1007/s00222-010-0298-z
[3] G. Pappas, M. Rapoport
Φ-modules and coefficient spaces
Mosc. Math. J. , 9: (3): 625--663, back matter
DOI: 10.17323/1609-4514-2009-9-3-625-663
[4] G. Pappas, M. Rapoport
Twisted loop groups and their affine flag varieties
With an appendix by T. Haines and Rapoport
Adv. Math. , 219: (1): 118--198
DOI: 10.1016/j.aim.2008.04.006
[5] Stephen S. Kudla, Michael Rapoport, Tonghai Yang
Modular forms and special cycles on Shimura curves
of Annals of Mathematics Studies : x+373
Publisher: Princeton University Press, Princeton, NJ
ISBN: 978-0-691-12551-0; 0-691-12551-1
DOI: 10.1515/9781400837168
[6] M. Rapoport, Th. Zink
Period spaces for p-divisible groups
of Annals of Mathematics Studies : xxii+324
Publisher: Princeton University Press, Princeton, NJ
ISBN: 0-691-02782-X; 0-691-02781-1
DOI: 10.1515/9781400882601
[7] G. Laumon, M. Rapoport, U. Stuhler
{D}-elliptic sheaves and the Langlands correspondence
Invent. Math. , 113: (2): 217--338
DOI: 10.1007/BF01244308

Publication List

MathSciNet Publication List (external link)


• Duke Math. J. (Associate Editor, 1995 - 2000)
• Ergebnisse der Mathematik, Springer Verlag (Editor, 1998 - 2003)
• International Mathematics Research Notices (Editor, 2003 - 2019)
• Algebra and Number Theory (Editor, since 2015)
• Epiga (Editor, 2016 - 2019)



Akademiestipendium of the VW-foundation


Leibniz Prize


Prix Gay-Lussac/Humboldt of the French Ministry of Education


Member of the Leopoldina (German National Academy of Sciences)


Heinz Hopf Prize


Teaching prize of the University of Bonn


Staudt Prize


Member of the Academia Europaea

Selected Invited Lectures


Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA


Invited speaker, International Congress of Mathematicians, Zürich, Switzerland


Invited plenary speaker at Annual Conference of DMV, Ulm


Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA


Heinz Hopf Lectures, ETH Zürich, Switzerland


Torsten Wedhorn (2005)

Ulrich Görtz (2006)

Sascha Orlik (2007)

Eva Viehmann (2011)

Eugen Hellmann (2016)

Selected PhD students

Torsten Wedhorn (1998): “Ordinariness in Good Reductions of Schimura Varieties of PEL-Type”,
now Professor, TU Darmstadt

Sascha Orlik (1999): “Kohomologie von Periodenbereichen”,
now Professor, University of Wuppertal

Ulrich Görtz (2000): “On the flatness of certain Shimura varieties of PEL-Type”,
now Professor, University of Duisburg-Essen

Eva Viehmann (2005): “On affine Deligne-Lusztig varieties for GL_n”,
now Professor, TU Munich

Ulrich Terstiege (2009): “Intersections of Arithmetic Hirzebruch-Zagier Cycles”,
now Scientific Staff, RWTH Aachen

Eugen Hellmann (2011): “On arithmetic families of filtered f-modules and crystalline representations”,
now Professor, University of Münster

Peter Scholze (2012): “Perfectoid Spaces”,
now Professor (Hausdorff Chair), University of Bonn

Timo Richarz (2014): “On geometric Satake equivalences”,
now Scientific Staff, University of Duisburg-Essen

Daniel Kirch (2015): “Construction of a Rapoport-Zink space for split {\rm GU}(1, 1) in the ramified 2-adic case”,
now DFG-fellow, University of Paris VI, France

Andreas Mihatsch (2016): “Relative RZ-spaces and the Arithmetic Fundamental Lemma”

Supervised Theses

  • Master theses: 3
  • Diplom theses: 19
  • PhD theses: 14
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