

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  Since 2003  Professor (C4), 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 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.


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[ 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 File: http://http://dx.doi.org/10.1007/s002220100298z[3] JeanFrancois 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 [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 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
phimodules 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



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


1992  Leibniz Prize  2000  Prix GayLussac/Humboldt  2011  Heinz Hopf Prize 


1992  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 


Torsten Wedhorn (2005), now Professor, TU Darmstadt
Ulrich Görtz (2006), now Professor, University of DuisburgEssen
Sascha Orlik (2007), now Professor, University of Wuppertal
Eva Viehmann (2011), now Professor, TU Munich


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


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


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