Peter Scholze

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Peter Scholze is a German mathematician born on December 11, 1987, in Dresden, Germany. He is renowned for his groundbreaking work in arithmetic geometry and algebraic topology. Scholze is particularly famous for developing the theory of perfectoid spaces, which has had profound implications in number theory and related fields.


Educational Background and Career:



  • Early Education: Scholze showed exceptional talent in mathematics from a young age. He participated in the International Mathematical Olympiad, earning gold medals in 2005 and 2006.

  • University of Bonn: He pursued his undergraduate and doctoral studies at the University of Bonn. He completed his Ph.D. in 2012 under the supervision of Michael Rapoport.

  • Academic Positions: At just 24 years old, Scholze became a full professor at the University of Bonn, one of the youngest in German history.

  • Director at the Max Planck Institute: In 2018, he became a director at the Max Planck Institute for Mathematics in Bonn.


Contributions to Mathematics:



  • Perfectoid Spaces: Introduced the concept of perfectoid spaces, which has advanced the understanding of the connections between arithmetic geometry and p-adic analysis.

  • p-adic Geometry: His work has led to significant progress in the Langlands program, particularly in the area of p-adic geometry.

  • Publications and Lectures: Scholze has published numerous influential papers and is known for his clear and insightful lectures.


Awards and Recognition:



  • Fields Medal (2018): Often referred to as the "Nobel Prize of Mathematics," awarded for his outstanding contributions to arithmetic algebraic geometry.

  • Clay Research Award (2014): Recognizing his breakthroughs in mathematics.

  • Cole Prize in Algebra (2015): Awarded by the American Mathematical Society for his notable work in algebra.

  • Leibniz Prize (2016): One of Germany's most prestigious research prizes.

  • Memberships: Elected to several academies, including the German National Academy of Sciences Leopoldina and as a foreign associate of the National Academy of Sciences in the USA.


Impact and Legacy:


Peter Scholze is considered one of the leading mathematicians of his generation. His innovative ideas have opened new avenues of research and inspired mathematicians worldwide. Beyond his research, he is involved in teaching and mentoring young mathematicians, contributing to the future of the discipline.

All published works
Action Title Year Authors
+ PDF Chat Geometrization of the local Langlands correspondence, motivically 2025 Peter Scholze
+ PDF Chat Geometric Eisenstein series I: finiteness theorems 2024 Linus Hamann
David J. Hansen
Peter Scholze
+ PDF Chat A note on higher almost ring theory 2024 Fabian Hebestreit
Peter Scholze
+ PDF Chat On the generic part of the cohomology of non-compact unitary Shimura varieties 2024 Ana Caraiani
Peter Scholze
+ Purity for flat cohomology 2023 Kęstutis Česnavičius
Peter Scholze
+ PDF Relative perversity 2023 David J. Hansen
Peter Scholze
+ PDF Chat Potential automorphy over CM fields 2023 Patrick B. Allen
Frank Calegari
Ana Caraiani
Toby Gee
David Helm
Bao Le Hung
James Newton
Peter Scholze
Richard Taylor
Jack A. Thorne
+ PDF Chat Prismatic $F$-crystals and crystalline Galois representations 2023 Bhargav Bhatt
Peter Scholze
+ PDF Chat Prisms and prismatic cohomology 2022 Bhargav Bhatt
Peter Scholze
+ Relative Perversity. 2021 David J. Hansen
Peter Scholze
+ Arithmetic Geometry 2021 Герд Фалтингс
A. J. de Jong
Peter Scholze
+ Geometrization of the local Langlands correspondence 2021 L Fargues
Peter Scholze
+ Relative Perversity 2021 David Hansen
Peter Scholze
+ Prismatic $F$-crystals and crystalline Galois representations 2021 Bhargav Bhatt
Peter Scholze
+ Purity for flat cohomology 2020 Kęstutis Česnavičius
Peter Scholze
+ Purity for flat cohomology 2020 Kęstutis Česnavičius
Peter Scholze
+ Purity for flat cohomology 2020 Kęstutis Česnavičius
Peter Scholze
+ Purity for flat cohomology 2020 Kęstutis Česnavičius
Peter Scholze
+ Lecture 22. Vector bundles and G-torsors on the relative Fargues-Fontaine curve 2020 Peter Scholze
Jared Weinstein
+ Lecture 16. Drinfeld's lemma for diamonds 2020 Peter Scholze
Jared Weinstein
+ Lecture 4. Examples of adic spaces 2020 Peter Scholze
Jared Weinstein
+ Lecture 18. v-sheaves associated with perfect and formal schemes 2020 Peter Scholze
Jared Weinstein
+ Lecture 6. Perfectoid rings 2020 Peter Scholze
Jared Weinstein
+ Lecture 20. Families of affine Grassmannians 2020 Peter Scholze
Jared Weinstein
+ Lecture 23. Moduli spaces of shtukas 2020 Peter Scholze
Jared Weinstein
+ Lecture 5. Complements on adic spaces 2020 Peter Scholze
Jared Weinstein
+ Lecture 10. Diamonds associated with adic spaces 2020 Peter Scholze
Jared Weinstein
+ Lecture 2. Adic spaces 2020 Peter Scholze
Jared Weinstein
+ Lecture 25. Integral models of local Shimura varieties 2020 Peter Scholze
Jared Weinstein
+ Lecture 7. Perfectoid spaces 2020 Peter Scholze
Jared Weinstein
+ Lecture 24. Local Shimura varieties 2020 Peter Scholze
Jared Weinstein
+ Lecture 3. Adic spaces II 2020 Peter Scholze
Jared Weinstein
+ Lecture 19. The B+dR-affine Grassmannian 2020 Peter Scholze
Jared Weinstein
+ Berkeley Lectures on p-adic Geometry 2020 Peter Scholze
Jared Weinstein
+ Local Shimura varieties 2020 Peter Scholze
Jared Weinstein
+ Affine flag varieties 2020 Peter Scholze
Jared Weinstein
+ Mixed-characteristic shtukas 2020 Peter Scholze
Jared Weinstein
+ The v-topology 2020 Peter Scholze
Jared Weinstein
+ Diamonds associated with adic spaces 2020 Peter Scholze
Jared Weinstein
+ Examples of diamonds 2020 Peter Scholze
Jared Weinstein
+ Families of affine Grassmannians 2020 Peter Scholze
Jared Weinstein
+ Adic spaces II 2020 Peter Scholze
Jared Weinstein
+ Drinfeld’s lemma for diamonds 2020 Peter Scholze
Jared Weinstein
+ Examples of adic spaces 2020 Peter Scholze
Jared Weinstein
+ Integral models of local Shimura varieties 2020 Peter Scholze
Jared Weinstein
+ Vector bundles and G-torsors on the relative Fargues-Fontaine curve 2020 Peter Scholze
Jared Weinstein
+ The BdR+-affine Grassmannian 2020 Peter Scholze
Jared Weinstein
+ v-sheaves associated with perfect and formal schemes 2020 Peter Scholze
Jared Weinstein
+ Complements on adic spaces 2020 Peter Scholze
Jared Weinstein
+ Moduli spaces of shtukas 2020 Peter Scholze
Jared Weinstein
+ Berkeley Lectures on p-adic Geometry 2020 Peter Scholze
Jared Weinstein
+ Adic spaces 2020 Peter Scholze
Jared Weinstein
+ Perfectoid rings 2020 Peter Scholze
Jared Weinstein
+ Diamonds II 2020 Peter Scholze
Jared Weinstein
+ Perfectoid spaces 2020 Peter Scholze
Jared Weinstein
+ Shtukas with one leg III 2020 Peter Scholze
Jared Weinstein
+ Diamonds 2020 Peter Scholze
Jared Weinstein
+ Berkeley Lectures on p-adic Geometry 2020 Peter Scholze
Jared Weinstein
+ Introduction 2020 Peter Scholze
Jared Weinstein
+ Perfectoid Shimura varieties 2019 Bhargav Bhatt
Ana Caraiani
Kiran S. Kedlaya
Peter Scholze
Jared Weinstein
+ Adic spaces 2019 Bhargav Bhatt
Ana Caraiani
Kiran S. Kedlaya
Peter Scholze
Jared Weinstein
+ <i>p</i>-ADIC GEOMETRY 2019 Peter Scholze
+ Topological Hochschild homology and integral p $p$ -adic Hodge theory 2019 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Arbeitsgemeinschaft: Topological Cyclic Homology 2019 Lars Hesselholt
Peter Scholze
+ PDF Correction to “On topological cyclic homology” 2019 Thomas Nikolaus
Peter Scholze
+ Foliations with positive slopes and birational stability of orbifold cotangent bundles . Fourier interpolation on the real line . Joinings of higher rank torus actions on homogeneous spaces . Categorical actions on unipotent representations of finite unitary groups . Topological Hochschild homology and integral ρ-adic Hodge theory 2019 Frédéric Campana
Mihai Păun
Danylo Radchenko
Maryna Viazovska
Manfred Einsiedler
Elon Lindenstrauss
Olivier Dudas
Michela Varagnolo
Éric Vasserot
Bhargav Bhatt
+ Prisms and Prismatic Cohomology 2019 Bhargav Bhatt
Peter Scholze
+ Purity for flat cohomology 2019 Kęstutis Česnavičius
Peter Scholze
+ On the generic part of the cohomology of non-compact unitary Shimura varieties 2019 Ana Caraiani
Peter Scholze
+ PDF Chat The pro-étale topology for schemes 2018 Bhargav Bhatt
Peter Scholze
+ Integral p $p$ -adic Hodge theory 2018 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Topological Hochschild homology and integral $p$-adic Hodge theory 2018 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ PDF On topological cyclic homology 2018 Thomas Nikolaus
Peter Scholze
+ On the p-adic cohomology of the Lubin-Tate tower 2018 Peter Scholze
+ PDF Chat Topological Realisations of Absolute Galois Groups 2018 Robert A. Kucharczyk
Peter Scholze
+ Measure concentration and the weak Pinsker property . Integral models of Shimura varieties with parahoric level structure . Integral p-adic Hodge theory 2018 Tim Austin
Mark Kisin
G. Pappas
Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Potential automorphy over CM fields 2018 Patrick B. Allen
Frank Calegari
Ana Caraiani
Toby Gee
David Helm
Bao V. Le Hung
James Newton
Peter Scholze
Richard G. Taylor
Jack A. Thorne
+ PDF Canonical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-deformations in arithmetic geometry 2017 Peter Scholze
+ $p$-adic geometry 2017 Peter Scholze
+ PDF Chat Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ Etale cohomology of diamonds 2017 Peter Scholze
+ PDF Chat On the generic part of the cohomology of compact unitary Shimura varieties 2017 Ana Caraiani
Peter Scholze
+ Arithmetic Geometry 2017 Герд Фалтингс
A. J. de Jong
Peter Scholze
+ Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ Arbeitsgemeinschaft: The Geometric Langlands Conjecture 2017 L Fargues
Dennis Gaitsgory
Peter Scholze
Kari Vilonen
+ PDF Chat Étale Cohomology of Diamonds 2017 Peter Scholze
+ p-Adic Geometry 2017 Peter Scholze
+ On topological cyclic homology 2017 Thomas Nikolaus
Peter Scholze
+ Etale cohomology of diamonds 2017 Peter Scholze
+ Vanishing theorems for perverse sheaves on abelian varieties, revisited 2017 Bhargav Bhatt
Christian Schnell
Peter Scholze
+ $p$-adic geometry 2017 Peter Scholze
+ PDF Chat Projectivity of the Witt vector affine Grassmannian 2016 Bhargav Bhatt
Peter Scholze
+ Topological realisations of absolute Galois groups 2016 Robert A. Kucharczyk
Peter Scholze
+ Canonical q-deformations in arithmetic geometry 2016 Peter Scholze
+ Integral p-adic Hodge theory 2016 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ PDF -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES – CORRIGENDUM 2016 Peter Scholze
+ PDF Canonical q-Deformations in Arithmetic Geometry 2016 Peter Scholze
+ Integral p-adic Hodge theory 2016 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Topological realisations of absolute Galois groups 2016 Robert A. Kucharczyk
Peter Scholze
+ Canonical q-deformations in arithmetic geometry 2016 Peter Scholze
+ Perfectoid Shimura varieties 2015 Peter Scholze
+ On the generic part of the cohomology of compact unitary Shimura varieties 2015 Ana Caraiani
Peter Scholze
+ PDF Chat On torsion in the cohomology of locally symmetric varieties 2015 Peter Scholze
+ Integral $p$-adic Hodge theory - announcement 2015 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ Projectivity of the Witt vector affine Grassmannian 2015 Bhargav Bhatt
Peter Scholze
+ On the p-adic cohomology of the Lubin-Tate tower 2015 Peter Scholze
+ PDF Integral $p$-adic Hodge theory — announcement 2015 BhuwanC Bhatt
Matthew Morrow
Peter Scholze
+ The Pro-étale topology for schemes 2015 Bhargav Bhatt
Peter Scholze
+ PDF Chat On Torsion in the Cohomology of Locally Symmetric Varieties 2015 Peter Scholze
+ Projectivity of the Witt vector affine Grassmannian 2015 Bhargav Bhatt
Peter Scholze
+ Integral $p$-adic Hodge theory - announcement 2015 Bhargav Bhatt
Matthew Morrow
Peter Scholze
+ On the generic part of the cohomology of compact unitary Shimura varieties 2015 Ana Caraiani
Peter Scholze
+ On torsion in the cohomology of locally symmetric varieties 2013 Peter Scholze
+ Perfectoid Spaces: A survey 2013 Peter Scholze
+ PDF Moduli of $p$-divisible groups 2013 Peter Scholze
Jared Weinstein
+ PDF -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES 2013 Peter Scholze
+ On torsion in the cohomology of locally symmetric varieties 2013 Peter Scholze
+ Perfectoid Spaces: A survey 2013 Peter Scholze
+ The pro-étale topology for schemes 2013 Bhargav Bhatt
Peter Scholze
+ Moduli of p-divisible groups 2012 Peter Scholze
Jared Weinstein
+ PDF Chat On the cohomology of compact unitary group Shimura varieties at ramified split places 2012 Peter Scholze
Sug Woo Shin
+ The Langlands-Kottwitz method and deformation spaces of 𝑝-divisible groups 2012 Peter Scholze
+ PDF Chat The Local Langlands Correspondence for GL n over p-adic fields 2012 Peter Scholze
+ PDF Chat The Langlands-Kottwitz approach for some simple Shimura varieties 2012 Peter Scholze
+ Perfectoid Spaces 2012 Peter Scholze
+ On the cohomology of compact unitary group Shimura varieties at ramified split places 2012 Peter Scholze
Sug Woo Shin
+ p-adic Hodge theory for rigid-analytic varieties 2012 Peter Scholze
+ PDF Perfectoid spaces: A survey 2012 Peter Scholze
+ PDF Chat p-Adic Hodge Theory for Rigid-Analytic Varieties 2012 Peter Scholze
+ p-adic Hodge theory for rigid-analytic varieties 2012 Peter Scholze
+ Moduli of p-divisible groups 2012 Peter Scholze
Jared Weinstein
+ Simply-laced isomonodromy systems . On the functions counting walks with small steps in the quarter plane . The structure of approximate groups . On stably free modules over affine algebras . Perfectoid spaces 2012 Philip Boalch
Irina Kurkova
Kilian Raschel
Emmanuel Breuillard
Ben Green
Terence Tao
Jean Fasel
Ravi A. Rao
Richard G. Swan
Peter Scholze
+ Perfectoid spaces 2011 Peter Scholze
+ On the cohomology of compact unitary group Shimura varieties at ramified split places 2011 Peter Scholze
Sug Woo Shin
+ The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups 2011 Peter Scholze
+ On the cohomology of compact unitary group Shimura varieties at ramified split places 2011 Peter Scholze
Sug Woo Shin
+ The Langlands-Kottwitz method and deformation spaces of $p$-divisible groups 2011 Peter Scholze
+ PDF Chat The Langlands-Kottwitz approach for the modular curve 2010 Peter Scholze
+ The Local Langlands correspondence for $\GL_n$ over $p$-adic fields 2010 Peter Scholze
+ The Langlands-Kottwitz approach for some simple Shimura Varieties 2010 Peter Scholze
+ The Langlands-Kottwitz approach for the modular curve 2010 Peter Scholze
+ The Langlands-Kottwitz approach for some simple Shimura Varieties 2010 Peter Scholze
+ The Local Langlands correspondence for $\GL_n$ over $p$-adic fields 2010 Peter Scholze
+ The Langlands-Kottwitz approach for the modular curve 2010 Peter Scholze
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ Étale Cohomology of Rigid Analytic Varieties and Adic Spaces 1996 Roland Huber
23
+ PDF -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES 2013 Peter Scholze
13
+ Relative p-adic Hodge theory: Foundations 2013 Kiran S. Kedlaya
Ruochuan Liu
12
+ PDF Chat On torsion in the cohomology of locally symmetric varieties 2015 Peter Scholze
11
+ On the λ-adic representations associated to some simple Shimura varieties 1992 Robert Kottwitz
11
+ PDF Moduli of $p$-divisible groups 2013 Peter Scholze
Jared Weinstein
11
+ PDF Galois representations arising from some compact Shimura varieties 2011 Sug Woo Shin
10
+ Almost Ring Theory 2003 Ofer Gabber
Lorenzo Ramero
10
+ PDF Smoothness, semi-stability and alterations 1996 A. J. de Jong
9
+ Period Spaces for p-divisible Groups 1995 Michael Rapoport
Thomas Zink
9
+ The Geometry and Cohomology of Some Simple Shimura Varieties. 2001 Michael Harris
Richard Taylor
Vladimir G. Berkovich
9
+ PDF Chat Groupes p-Divisibles, Groupes Finis et Modules Filtres 2000 Christophe Breuil
8
+ PDF 𝑝-adic Hodge theory 1988 Герд Фалтингс
8
+ Almost étale extensions 2002 Герд Фалтингс
8
+ Perfectoid Spaces 2012 Peter Scholze
7
+ The Pro-étale topology for schemes 2015 Bhargav Bhatt
Peter Scholze
7
+ Non-Archimedean Analysis 1984 Siegfried Bosch
Ulrich Güntzer
Reinhold Remmert
7
+ Notes on Crystalline Cohomology. 2015 Pierre Berthelot
Arthur Ogus
7
+ Crystalline representations and F-crystals 2007 Mark Kisin
6
+ Higher Topos Theory 2009 Jacob Lurie
6
+ PDF Chat The conjectural connections between automorphic representations and Galois representations 2014 Kevin Buzzard
Toby Gee
6
+ PDF Construction of automorphic Galois representations, II 2013 Gaëtan Chenevier
Michael Harris
6
+ Shimura varieties and twisted orbital integrals 1984 Robert Kottwitz
6
+ PDF None 2002 Thomas J. Haines
B. C. Ngô
6
+ On local properties of non-Archimedean analytic spaces 2000 Michael Temkin
6
+ PDF Points on some Shimura varieties over finite fields 1992 Robert Kottwitz
5
+ p-Divisible Groups 1967 John Tate
5
+ PDF Représentations p-adiques cristallines et de de Rham dans le cas relatif 2008 Olivier Brinon
5
+ PDF Chat Projectivity of the Witt vector affine Grassmannian 2016 Bhargav Bhatt
Peter Scholze
5
+ PDF Chat Local-global compatibility and the action of monodromy on nearby cycles 2012 Ana Caraiani
5
+ La conjecture de Weil. I 1974 Pierre Deligne
5
+ PDF Perfectoid spaces: A survey 2012 Peter Scholze
5
+ �ber die lokale Zetafunktion von Shimuravariet�ten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik 1982 Michael Rapoport
Th. Zink
5
+ PDF Absolute cohomological purity 1984 R. W. Thomason
5
+ PDF None 1997 Robert Kottwitz
5
+ PDF Solutions d'équations à coefficients dans un anneau hensélien 1973 Renée Elkik
5
+ Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique 2000 Guy Henniart
5
+ Compatibility of local and global Langlands correspondences 2006 Richard Taylor
Teruyoshi Yoshida
5
+ p-adic étale cohomology and crystalline cohomology in the semi-stable reduction case 1999 Takeshi Tsuji
5
+ Continuous valuations 1993 R. Huber
5
+ Der Endlichkeitssatz f�r eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie 1967 Reinhardt Kiehl
5
+ PDF Chat On the cohomology of compact unitary group Shimura varieties at ramified split places 2012 Peter Scholze
Sug Woo Shin
5
+ Coverings of p-adic period domains 2010 Герд Фалтингс
4
+ PDF Induced representations of reductive ${\germ p}$-adic groups. I 1977 I. N. Bernstein
Andrei Zelevinsky
4
+ Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties 2012 Kai‐Wen Lan
Junecue Suh
4
+ PDF None 1997 J. L. Waldspurger
4
+ PDF Chat The de Rham-Witt complex and 𝑝-adic vanishing cycles 2005 Thomas Geisser
Lars Hesselholt
4
+ PDF Les suites spectrales associées au complexe de de Rham-Witt 1983 Luc Illusie
Michel Raynaud
4
+ Integral p-adic Hodge theory 2016 Bhargav Bhatt
Matthew Morrow
Peter Scholze
4
+ The fundamental lemma for stable base change 1990 Laurent Clozel
4