Profile
Profile

Prof. Dr. Peter Scholze

Hausdorff Chair

E-mail: scholze(at)math.uni-bonn.de
Phone: +49 228 73 62237
Homepage: http://www.math.uni-bonn.de/people/scholze/
Room: 4.029
Location: Mathematics Center
Institute: Mathematical Institute
Bonn International Graduate School - BIGS
Research Areas: Research Area DE
Former Research Area D
Former Research Area E
Date of birth: 11.Dec 1987

Academic Career

2010

Master, University of Bonn

2012

Dr. rer. nat., University of Bonn

Since 2012

Hausdorff Chair (W3), University of Bonn

Research Profile

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 p-adic Hodge theory.

My own contributions to these questions include the construction of Galois representations associated for example with torsion classes on hyperbolic 3-manifolds, and the development of a geometric framework underlying much of p-adic 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 p-adic fields, and I hope to use this to obtain new results on the local Langlands conjecture for general groups over p-adic fields. On the other hand, in work with Bhatt and Morrow, we found new cohomological invariants of arithmetic varieties, which lead to a surprising q-deformation of de Rham cohomology, which I plan to study further.

Contribution to Research Areas

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 p-adic automorphic forms with Galois representations.

Selected Publications

[1] Bhargav Bhatt, Peter Scholze
Projectivity of the Witt vector affine Grassmannian
Invent. Math. , 209: (2): 329--423
2017
DOI: 10.1007/s00222-016-0710-4
[2] Peter Scholze
On torsion in the cohomology of locally symmetric varieties
Ann. of Math. (2) , 182: (3): 945--1066
2015
DOI: 10.4007/annals.2015.182.3.3
[3] Bhargav Bhatt, Peter Scholze
The pro-étale topology for schemes
Astérisque (369): 99--201
2015
ISBN: 978-2-85629-805-3
[4] Peter Scholze, Jared Weinstein
Moduli of p-divisible groups
Camb. J. Math.
, 1: (2): 145--237
2013
DOI: 10.4310/CJM.2013.v1.n2.a1
[5] Peter Scholze
p-adic Hodge theory for rigid-analytic varieties
Forum Math. Pi , 1: : e1, 77
2013
DOI: 10.1017/fmp.2013.1
[6] Peter Scholze
The local Langlands correspondence for GLn over p-adic fields
Invent. Math. , 192: (3): 663--715
2013
DOI: 10.1007/s00222-012-0420-5
[7] Peter Scholze, Sug Woo Shin
On the cohomology of compact unitary group Shimura varieties at ramified split places
J. Amer. Math. Soc. , 26: (1): 261--294
2013
DOI: 10.1090/S0894-0347-2012-00752-8
[8] Peter Scholze
Perfectoid spaces
Publ. Math. Inst. Hautes Études Sci. , 116: : 245--313
2012
DOI: 10.1007/s10240-012-0042-x

Publication List

Editorships

• Journal of the AMS
• Compositio Math

Awards

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 Berlin-Brandenburg Academy of Sciences and Humanities

2017

Ordinary Member of the Academy of Science and Literature, Mainz

Selected Invited Lectures

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

Download Profile