Prof. Dr. Michael Rapoport

E-mail: rapoport(at)
Phone: +49 228 73 7793
Room: 1.031
Location: Mathematics Center
Institute: Mathematical Institute
Research Areas: Former Research Area D (Leader)
Research Area DE
Former Research Area E
Former Research Area F
Birthdate: 02.Oct 1948
Mathscinet-Number: 144965

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 (C3), University of Wuppertal

1996 - 2003

Professor (C4), University of Cologne

Since 2003

Professor (C4), University of Bonn

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 Shimura varieties and their local variants - from the point of view of constructing interesting Galois representations, of identifying algebraic cycles on them, and of studying their deformations.

Contribution to Research Areas

Former Research Area D
My contributions in this RA can be grouped into two main directions. First, there has been substantial progress in my joint project with S. Kudla in giving arithmetic interpretations of the Fourier coefficients of Eisenstein series. The case of the modular curve with no ramifications has been completely solved and is documented in the monograph [1] with S. Kudla and T. Yang. The basis for our results are the theory of Gross/Keating. In my seminar we elaborated an up-to-date account of this theory. Recently Kudla and I started to develop an analogous theory for the Shimura varieties associated to unitary groups [2].
Second, in the direction of Shimura varieties, I published a monograph [3] on the theory of period spaces with Dat and Orlik. It leads from the elementary theory of filtered vector spaces to the first published account of the determination of the Euler-Poincaré characteristic of p-adic period domains.
Former Research Area E
I developed further, in collaboration and close contact with G. Pappas and B. Smithling, the theory of local models of Shimura varieties. The paper [4] treats the case of ramified unitary groups, and states the highly relevant “coherence conjecture” which has been proved recently in spectacular work of X. Zhu. Smithling has proved the topological flatness conjecture of loc.cit.
Another topic developed in [5] is the theory of <br>mathcal G-bundles on algebraic curves. Some conjectures of loc. cit. have been proved by J. Heinloth.
Former Research Area F
I developed with G. Pappas [6] a theory of algebraic loop groups, generalizing the theory of Faltings to the non-constant, or twisted, case. In [7], Pappas and I gave a new framework for moduli spaces of Kisin modules it coefficient spaces, with possible applications to deformation problems of Galois representations.
Research Area DE

Selected Publications

[1] 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
[2] Stephen Kudla, Michael Rapoport
Special cycles on unitary Shimura varieties I. Unramified local theory
Inventiones Mathematicae : 1-54
Publisher: Springer Berlin / Heidelberg
ISSN: 0020-9910
File: http://
[3] Jean-Francois Dat, Sascha Orlik, Michael Rapoport
Period domains over finite and p-adic fields
of Cambridge Tracts in Mathematics : xxii+372
Publisher: Cambridge University Press, Cambridge
ISBN: 978-0-521-19769-4
[4] G. Pappas, M. Rapoport
Local models in the ramified case. III. Unitary groups
J. Inst. Math. Jussieu
, 8: (3): 507--564
ISSN: 1474-7480
DOI: 10.1017/S1474748009000139
[5] Georgios Pappas, Michael Rapoport
Some questions about G-bundles on curves
Algebraic and arithmetic structures of moduli spaces (Sapporo 2007)
of Adv. Stud. Pure Math. : 159--171
Publisher: Math. Soc. Japan, Tokyo
[6] 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
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.04.006
[7] G. Pappas, M. Rapoport
phi-modules and coefficient spaces
Mosc. Math. J. , 9: (3): 625--663, back matter
ISSN: 1609-3321
[8] Avner Ash, David Mumford, Michael Rapoport, Yung-Sheng Tai
Smooth compactifications of locally symmetric varieties
With the collaboration of Peter Scholze
Cambridge Mathematical Library : x+230
Publisher: Cambridge University Press, Cambridge
ISBN: 978-0-521-73955-9
DOI: 10.1017/CBO9780511674693
[9] 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

Publication List


• Duke Math. Journal (Associate Editor, 1995 - 2000)
• Ergebnisse Series Springer Verlag (Editor, 1998 - 2003)
• International Mathematics Research Notices (Editor, since 2003)



Leibniz Prize


Prix Gay-Lussac/Humboldt


Heinz Hopf Prize

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


Torsten Wedhorn (2005), now Professor, TU Darmstadt

Ulrich Görtz (2006), now Professor, University of Duisburg-Essen

Sascha Orlik (2007), now Professor, University of Wuppertal

Eva Viehmann (2011), now Professor, TU Munich

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 Postdoc, University of Bonn

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

Supervised Theses

  • Master theses: 3, currently 2
  • Diplom theses: 19, currently 2
  • PhD theses: 9, currently 2
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