

2010  Master, University of Bonn  2012  Dr. rer. nat., University of Bonn  Since 2012  Hausdorff Chair (W3), University of Bonn 


My research is at the intersection of number theory and algebraic geometry, and deals with the basic questions and structures that underly our modern understanding of diophantine equations. This concerns on the one hand the Langlands program, which connects objects from arithmetic geometry, such as elliptic curves over number fields, with analytic or topological objects, such as modular forms or the cohomology of hyperbolic manifolds. On the other hand, this concerns the cohomological invariants attached to arithmetic varieties themselves, which forms the subject of Hodge theory, or more particularly padic Hodge theory.
My own contributions to these questions include the construction of Galois representations associated for example with torsion classes on hyperbolic 3manifolds, and the development of a geometric framework underlying much of padic Hodge theory, in the form of perfectoid spaces. In the future, I plan to pursue these questions. In particular, building on perfectoid spaces, I want to transport some machinery from the geometric Langlands program to the case of padic fields, and I hope to use this to obtain new results on the local Langlands conjecture for general groups over padic fields. On the other hand, in work with Bhatt and Morrow, we found new cohomological invariants of arithmetic varieties, which lead to a surprising qdeformation of de Rham cohomology, which I plan to study further.


Research Area DE I obtained new results on the geometry of moduli spaces of abelian varieties, by showing that they attain the structure of a perfectoid space after increasing the level at p. This was used to obtain new results on modular and automorphic forms, and in particular on the relation of padic automorphic forms with Galois representations,[1]. Recently, we were able to give more precise bounds on the cohomological degrees in which torsion can appear [2], leading to potential automorphy results for elliptic curves over CM fields. 


[ 1] Peter Scholze
On torsion in the cohomology of locally symmetric varieties Ann. of Math. (2) , 182: (3): 9451066 2015 DOI: 10.4007/annals.2015.182.3.3[ 2] Ana Caraiani, Peter Scholze
On the generic part of the cohomology of compact unitary Shimura varieties Ann. of Math. (2) , 186: (3): 649766 2017 DOI: 10.4007/annals.2017.186.3.1[ 3] Bhargav Bhatt, Peter Scholze
Projectivity of the Witt vector affine Grassmannian Invent. Math. , 209: (2): 329423 2017 DOI: 10.1007/s0022201607104[ 4] Bhargav Bhatt, Peter Scholze
The proétale topology for schemes Astérisque (369): 99201 2015 ISBN: 9782856298053[5] Peter Scholze, Jared Weinstein
Moduli of pdivisible groups Camb. J. Math. , 1: (2): 145237 2013 DOI: 10.4310/CJM.2013.v1.n2.a1 [ 6] Peter Scholze
padic Hodge theory for rigidanalytic varieties Forum Math. Pi , 1: : e1, 77 2013 DOI: 10.1017/fmp.2013.1[ 7] Peter Scholze
The local Langlands correspondence for GL_{n} over padic fields Invent. Math. , 192: (3): 663715 2013 DOI: 10.1007/s0022201204205[ 8] Peter Scholze, Sug Woo Shin
On the cohomology of compact unitary group Shimura varieties at ramified split places J. Amer. Math. Soc. , 26: (1): 261294 2013 DOI: 10.1090/S089403472012007528[ 9] Peter Scholze
Perfectoid spaces Publ. Math. Inst. Hautes Études Sci. , 116: : 245313 2012 DOI: 10.1007/s102400120042x




• Journal of the AMS
• Compositio Math


2011  Clay Research Fellow  2012  Prix Peccot  2013  SASTRA Ramanujan Prize  2014  Clay Research Award  2015  Frank Nelson Cole Prize in Algebra from the American Mathematical Society  2015  Ostrowski Prize  2016  Prix Fermat  2016  Leibniz Prize  2016  EMS Prize  2016  Academy Prize of the BerlinBrandenburg Academy of Sciences and Humanities  2017  Ordinary Member of the Academy of Science and Literature, Mainz  2017  Ordinary Member of the BerlinBrandenburg Academy of Sciences and Humanities  2017  Member of the Leopoldina (German National Academy of Sciences) 


2012  Clay Research Conference, University of Oxford, England, UK  2012  Current Developments in Mathematics, Harvard University, Cambridge, MA, USA  2014  International Congress of Mathematicians, Seoul, South Korea  2014  Takagi Lectures, Tokyo, Japan  2015  Clay Research Conference, Oxford, UK  2015  Current Developments in Mathematics, Harvard University, Cambridge, MA, USA  2016  Plenary talk, European Congress of Mathematics, Berlin  2018  Plenary speaker, International Congress of Mathematicians, Rio de Janeiro, Brasil 


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