

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 (C3), 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 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 uptodate 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 EulerPoincaré characteristic of 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 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 nonconstant, 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



[ 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 2006 ISBN: 9780691125510; 0691125511 DOI: 10.1515/9781400837168[ 2] Stephen Kudla, Michael Rapoport
Special cycles on unitary Shimura varieties I. Unramified local theory 10.1007/s002220100298z Inventiones Mathematicae : 154 Publisher: Springer Berlin / Heidelberg 2010 ISSN: 00209910[3] JeanFrançois Dat, Sascha Orlik, Michael Rapoport
Period domains over finite and padic fields of Cambridge Tracts in Mathematics : xxii+372 Publisher: Cambridge University Press, Cambridge 2010 ISBN: 9780521197694 DOI: 10.1017/CBO9780511762482 [4] G. Pappas, M. Rapoport
Local models in the ramified case. III. Unitary groups J. Inst. Math. Jussieu , 8: (3): 507564 2009 ISSN: 14747480 DOI: 10.1017/S1474748009000139 [ 5] Georgios Pappas, Michael Rapoport
Some questions about \scr Gbundles on curves Algebraic and arithmetic structures of moduli spaces (Sapporo 2007) of Adv. Stud. Pure Math. : 159171 Publisher: Math. Soc. Japan, Tokyo 2010[ 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): 118198 2008 ISSN: 00018708 DOI: 10.1016/j.aim.2008.04.006[ 7] G. Pappas, M. Rapoport
Φmodules and coefficient spaces Mosc. Math. J. , 9: (3): 625663, back matter 2009 ISSN: 16093321[ 8] Avner Ash, David Mumford, Michael Rapoport, YungSheng Tai
Smooth compactifications of locally symmetric varieties With the collaboration of Peter Scholze Cambridge Mathematical Library : x+230 Publisher: Cambridge University Press, Cambridge 2010 ISBN: 9780521739559 DOI: 10.1017/CBO9780511674693[ 9] 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



• 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 GL_n”,
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 Postdoc, University of Bonn
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


Download Profile 