72 citations · 221 across the 16 of their papers we have counts for
28 papers
Lectures on Condensed Mathematics
Peter Scholze
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint wor…
Relative Perversity
David Hansen, Peter Scholze
We define and study a relative perverse -structure associated with any finitely presented morphism of schemes , with relative perversity equivalent to perversity of t…
Prismatic -crystals and crystalline Galois representations
Bhargav Bhatt, Peter Scholze
Let be a complete discretely valued field of mixed characteristic with perfect residue field. We prove that the category of prismatic -crystals on is…
Geometrization of the local Langlands correspondence
Laurent Fargues, Peter Scholze
Following the idea of [Far16], we develop the foundations of the geometric Langlands program on the Fargues--Fontaine curve. In particular, we define a category of -adic shea…
Purity for flat cohomology
Kestutis Cesnavicius, Peter Scholze
We establish the flat cohomology version of the Gabber-Thomason purity for étale cohomology: for a complete intersection Noetherian local ring and a commutative…
On the generic part of the cohomology of non-compact unitary Shimura varieties
Ana Caraiani, Peter Scholze
We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, exte…
Prisms and Prismatic Cohomology
Bhargav Bhatt, Peter Scholze
We introduce the notion of a prism, which may be regarded as a "deperfection" of the notion of a perfectoid ring. Using prisms, we attach a ringed site -- the prismatic site -- to…
Potential automorphy over CM fields
Patrick B. Allen, Frank Calegari, Ana Caraiani +7
Let be a CM number field. We prove modularity lifting theorems for regular -dimensional Galois representations over without any self-duality condition. We deduce that al…
Topological Hochschild homology and integral -adic Hodge theory
Bhargav Bhatt, Matthew Morrow, Peter Scholze
In mixed characteristic and in equal characteristic we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration…
-adic geometry
Peter Scholze
We discuss recent developments in -adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact -adic mani…
Etale cohomology of diamonds
Peter Scholze
Motivated by problems on the étale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands corresponde…
Vanishing theorems for perverse sheaves on abelian varieties, revisited
Bhargav Bhatt, Christian Schnell, Peter Scholze
We revisit some of the basic results of generic vanishing theory, as pioneered by Green and Lazarsfeld, in the context of constructible sheaves. Using the language of perverse shea…
Topological realisations of absolute Galois groups
Robert A. Kucharczyk, Peter Scholze
Let be a field of characteristic containing all roots of unity. We construct a functorial compact Hausdorff space whose profinite fundamental group agrees with the ab…
Canonical q-deformations in arithmetic geometry
Peter Scholze
In recent work with Bhatt and Morrow, we defined a new integral p-adic cohomology theory interpolating between etale and de Rham cohomology. An unexpected feature of this cohomolog…
Integral p-adic Hodge theory
Bhargav Bhatt, Matthew Morrow, Peter Scholze
We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, w…
Integral -adic Hodge theory - announcement
Bhargav Bhatt, Matthew Morrow, Peter Scholze
Given a proper, smooth (formal) scheme over the ring of integers of , we prove that if the crystalline cohomology of its special fibre is torsion-free then the -adi…
Projectivity of the Witt vector affine Grassmannian
Bhargav Bhatt, Peter Scholze
We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in W(k)[1/p]^n for a perfect field k of charactristic p, is representable by an ind-(perfect sch…
On the p-adic cohomology of the Lubin-Tate tower
Peter Scholze
We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representa…
The pro-étale topology for schemes
Bhargav Bhatt, Peter Scholze
We give a new definition of the derived category of constructible -adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a…
On torsion in the cohomology of locally symmetric varieties
Peter Scholze
The main result of this paper is the existence of Galois representations associated with the mod (or mod ) cohomology of the locally symmetric spaces for $\GL_n$ over a to…
Perfectoid Spaces: A survey
Peter Scholze
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to t…
Moduli of p-divisible groups
Peter Scholze, Jared Weinstein
We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, a…
p-adic Hodge theory for rigid-analytic varieties
Peter Scholze
We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingre…
Perfectoid spaces
Peter Scholze
We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting…