Homepage of Peter Scholze

Veranstaltungen

Papers/Preprints

• Relative Perversity (with David Hansen), Comm. Amer. Math. Soc. 3 (2023), 631--668.
• Prismatic F-crystals and crystalline Galois representations (with Bhargav Bhatt), Camb. J. Math. 11 (2023), no. 2, 507--562.
• Geometrization of the local Langlands correspondence (with Laurent Fargues), Preprint, 2021.
• Purity for flat cohomology (with Kestutis Cesnavicius), Preprint, 2019, to appear in Ann. Math.
• On the generic part of the cohomology of non-compact unitary Shimura varieties (with Ana Caraiani), to appear in Ann. Math.
• Prisms and prismatic cohomology (with Bhargav Bhatt), Ann. Math. (2) 196 (2022), No. 3, 1135--1275.
• Potential Automorphy over CM fields (with Patrick Allen, Frank Calegari, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Richard Taylor, Jack Thorne), Ann. Math. (2) 197 (2023), No. 3, 897--1113.
• Topological Hochschild homology and integral p-adic Hodge theory (with Bhargav Bhatt, Matthew Morrow), Publ. Math. de l'IHÉS 129 (2019), 199--310.
• Berkeley lectures on p-adic geometry (with Jared Weinstein), Annals of Math Studies 207.
• p-adic geometry, Proceedings of the ICM 2018.
• On topological cyclic homology (with Thomas Nikolaus), Acta Math 221 (2018), no. 2, 203--409.
• Étale cohomology of diamonds, Preprint, 2018.
• Vanishing theorems for perverse sheaves on abelian varieties, revisited (with Bhargav Bhatt, Christian Schnell), Selecta Math. (N.S.) 24 (2018), no. 1, 63--84.
• Topological realizations of absolute Galois groups (with Robert Kucharczyk), Cohomology of arithmetic groups, 201--288, Springer Proc. Math. Stat. 245.
• Canonical q-deformations in arithmetic geometry, Ann. Fac. Sci. Toulouse Math. (6) 26 (2017), no. 5, 1163--1192.
• Integral p-adic Hodge theory (with Bhargav Bhatt and Matthew Morrow), Publ. Math. de l'IHÉS 128 (2018), 219--397.
• On the generic part of the cohomology of compact unitary Shimura varieties (with Ana Caraiani), Annals of Mathematics (2) 186 (2017), no. 3, 649--766.
• Integral p-adic Hodge theory - Announcement (with Bhargav Bhatt, Matthew Morrow), Math. Res. Lett. 22 (2015), no. 6, 1601--1612.
• Projectivity of the Witt vector affine Grassmannian (with Bhargav Bhatt), Invent. Math. 209 (2017), no. 2, 329--423.
• On the p-adic cohomology of the Lubin-Tate tower, Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), no. 4, 811--863.
• Perfectoid spaces and their Applications, Proceedings of the ICM 2014.
• The pro-étale topology for schemes (with Bhargav Bhatt), Astérisque 369 (2015), 99--201.
• On torsion in the cohomology of locally symmetric varieties, Annals of Mathematics (2) 182 (2015), no. 3, 945--1066.
• Perfectoid spaces: A survey, Current Developments in Mathematics, 2012.
• Moduli of p-divisible groups (with Jared Weinstein), Cambridge Journal of Mathematics 1 (2013), 145--237.
• p-adic Hodge theory for rigid-analytic varieties, Forum of Mathematics, Pi, 1, e1, 2013. Erratum
• Perfectoid spaces, Publ. math. de l'IHÉS 116 (2012), no. 1, 245--313.
• On the cohomology of compact unitary group Shimura varieties at ramified split places (with Sug Woo Shin), J. Amer. Math. Soc. 26 (2013), no. 1, 261--294.
• The Langlands-Kottwitz method and deformation spaces of p-divisible groups, J. Amer. Math. Soc. 26 (2013), no. 1, 227--259.
• The Local Langlands Correspondence for GL_n over p-adic fields, Invent. Math. 192 (2013), no. 3, 663--715.
• The Langlands-Kottwitz method for some simple Shimura varieties, Invent. Math. 192 (2013), no. 3, 627--661.

Lecture Notes

• Six-Functor Formalisms, lecture notes for course WS 22/23.

• Condensed Mathematics and Complex Geometry, lecture notes for course SS 22.

• Geometrization of the local Langlands correspondence, lecture notes and videos.

• Lectures on Analytic Geometry, lecture notes for course WS 19/20.

• Lectures on Condensed Mathematics, lecture notes for course SS 19.