

1976  These d'Etat, University of ParisSud, 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  Since 2012  Professor (W3), University of Bonn 


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 RapoportZink 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 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 of integral models of Shimura varieties (the Newton stratification, the EkedahlOort stratification, the KottwitzRapoport 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 halfdimension on a RapoportZink 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 RapoportZink spaces on the underlying group theory. My recent theorem with T. Zink on the Drinfeld moduli problem of divisible groups deals in a special case related to 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 and apply this to the adic uniformization of certain Shimura curves. I want to understand the influence of exceptional isomorphisms between orthogonal groups and unitary groups on their associated RapoportZink 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 RapoportZink spaces and the conjectures of W. Zhang on arithmetic cycles of halfdimension. 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 modules which I started with G. Pappas and make progress after the recent contributions of M. Emerton/T. Gee.


Former Research Area D
 Former Research Area E
 Former Research Area F



[ 1] Michael Rapoport, Ulrich Terstiege, Wei Zhang
On the arithmetic fundamental lemma in the minuscule case Compos. Math. , 149: (10): 16311666 2013 DOI: 10.1112/S0010437X13007239[ 2] Stephen Kudla, Michael Rapoport
Special cycles on unitary Shimura varieties I. Unramified local theory Invent. Math. , 184: (3): 629682 2011 DOI: 10.1007/s002220100298z[ 3] G. Pappas, M. Rapoport
Φmodules and coefficient spaces Mosc. Math. J. , 9: (3): 625663, back matter 2009[ 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): 118198 2008 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 2006 ISBN: 9780691125510; 0691125511 DOI: 10.1515/9781400837168[ 6] M. Rapoport, Th. Zink
Period spaces for pdivisible groups of Annals of Mathematics Studies : xxii+324 Publisher: Princeton University Press, Princeton, NJ 1996 ISBN: 069102782X; 0691027811 DOI: 10.1515/9781400882601[ 7] G. Laumon, M. Rapoport, U. Stuhler
{D}elliptic sheaves and the Langlands correspondence Invent. Math. , 113: (2): 217338 1993 DOI: 10.1007/BF01244308[ 10] Jr., Dan Burns, Michael Rapoport
On the Torelli problem for kählerian K3 surfaces Ann. Sci. École Norm. Sup. (4) , 8: (2): 235273 1975



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


1991  Akademiestipendium of the VWfoundation  1992  Leibniz Prize  2000  Prix GayLussac/Humboldt of the French Ministry of Education  2003  Member of the Leopoldina (German National Academy of Sciences)  2011  Heinz Hopf Prize  2012  Teaching prize of the University of Bonn  2013  Staudt Prize  2013  Member of the Academia Europaea 


1993  Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA  1994  Invited speaker, International Congress of Mathematicians, Zürich, Switzerland  1995  Invited plenary speaker at Annual Conference of DMV, Ulm  2001  Distinguished Ordway visitor in Mathematics, University of Minnesota, Minneapolis, MN, USA  2011  Heinz Hopf Lectures, ETH Zürich, Switzerland 


Torsten Wedhorn (2005)
Ulrich Görtz (2006)
Sascha Orlik (2007)
Eva Viehmann (2011)
Eugen Hellmann (2016)


Torsten Wedhorn (1998): “Ordinariness in Good Reductions of Schimura Varieties of PELType”,
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 PELType”,
now Professor, University of DuisburgEssen
Eva Viehmann (2005): “On affine DeligneLusztig varieties for ”,
now Professor, TU Munich
Ulrich Terstiege (2009): “Intersections of Arithmetic HirzebruchZagier Cycles”,
now Scientific Staff, RWTH Aachen
Eugen Hellmann (2011): “On arithmetic families of filtered fmodules 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 DuisburgEssen
Daniel Kirch (2015): “Construction of a RapoportZink space for split in the ramified 2adic case”,
now DFGfellow, University of Paris VI, France
Andreas Mihatsch (2016): “Relative RZspaces and the Arithmetic Fundamental Lemma”


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


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