Zobrazeno 1 - 10
of 159
pro vyhledávání: '"Scholze, Peter"'
Autor:
Hebestreit, Fabian, Scholze, Peter
We explain a derived version of the basic construction of localisations of module categories by means of idempotent ideals, which lie at the heart of Faltings' almost ring theory.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2409.01940
Autor:
Hansen, David, Scholze, Peter
We define and study a relative perverse $t$-structure associated with any finitely presented morphism of schemes $f: X\to S$, with relative perversity equivalent to perversity of the restrictions to all geometric fibres of $f$. The existence of this
Externí odkaz:
http://arxiv.org/abs/2109.06766
Autor:
Bhatt, Bhargav, Scholze, Peter
Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$-crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline $G_K$-representa
Externí odkaz:
http://arxiv.org/abs/2106.14735
Autor:
Fargues, Laurent, Scholze, Peter
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 $\ell$-adic sheaves on the stack $\mathrm{Bun}_G$ of $G$-bundles on the Fargues--Fonta
Externí odkaz:
http://arxiv.org/abs/2102.13459
Autor:
Cesnavicius, Kestutis, Scholze, Peter
We establish the flat cohomology version of the Gabber-Thomason purity for \'{e}tale cohomology: for a complete intersection Noetherian local ring $(R, \mathfrak{m})$ and a commutative, finite, flat $R$-group $G$, the flat cohomology $H^i_{\mathfrak{
Externí odkaz:
http://arxiv.org/abs/1912.10932
Autor:
Caraiani, Ana, Scholze, Peter
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, extending our previous work to a non-compact case. The result applies even
Externí odkaz:
http://arxiv.org/abs/1909.01898
Autor:
Bhatt, Bhargav, Scholze, Peter
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 a $p$-adic formal scheme. The resulting cohomology theory specializes
Externí odkaz:
http://arxiv.org/abs/1905.08229
Autor:
Allen, Patrick B., Calegari, Frank, Caraiani, Ana, Gee, Toby, Helm, David, Hung, Bao V. Le, Newton, James, Scholze, Peter, Taylor, Richard, Thorne, Jack A.
Let $F$ be a CM number field. We prove modularity lifting theorems for regular $n$-dimensional Galois representations over $F$ without any self-duality condition. We deduce that all elliptic curves $E$ over $F$ are potentially modular, and furthermor
Externí odkaz:
http://arxiv.org/abs/1812.09999
In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded pieces are
Externí odkaz:
http://arxiv.org/abs/1802.03261
Autor:
Scholze, Peter
We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian varieties to a
Externí odkaz:
http://arxiv.org/abs/1712.03708