Purity for flat cohomology
K Česnavičius, P Scholze - Annals of Mathematics, 2024 - projecteuclid.org
We establish the flat cohomology version of the Gabber--Thomason purity for étale
cohomology: for a complete intersection Noetherian local ring (R,m) and a commutative …
cohomology: for a complete intersection Noetherian local ring (R,m) and a commutative …
Prismatic Dieudonné theory
J Anschütz, AC Le Bras - Forum of Mathematics, Pi, 2023 - cambridge.org
We define, for each quasisyntomic ring R (in the sense of Bhatt et al., Publ. Math. IHES 129
(2019), 199–310), a category of admissible prismatic Dieudonné crystals over R and a …
(2019), 199–310), a category of admissible prismatic Dieudonné crystals over R and a …
Generalised representations as q-connections in integral -adic Hodge theory
M Morrow, T Tsuji - arXiv preprint arXiv:2010.04059, 2020 - arxiv.org
We relate various approaches to coefficient systems in relative integral $ p $-adic Hodge
theory, working in the geometric context over the ring of integers of a perfectoid field. These …
theory, working in the geometric context over the ring of integers of a perfectoid field. These …
A PEL-type Igusa Stack and the -adic Geometry of Shimura Varieties
M Zhang - arXiv preprint arXiv:2309.05152, 2023 - arxiv.org
Let $(G, X) $ be a PEL-Shimura datum of type AC in Kottwitz's classification. Assume $ G_
{\mathbf {Q} _p} $ is unramified. We show that the good reduction locus of the infinite $ p …
{\mathbf {Q} _p} $ is unramified. We show that the good reduction locus of the infinite $ p …
l-Adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
P Hamacher, W Kim - Mathematische Annalen, 2019 - Springer
Abstract Let (G, X)(G, X) be a Shimura datum of Hodge type. Let p be an odd prime such that
G _ Q _p GQ p splits after a tamely ramified extension and p\not ∣| π _1 (G^ der)| p∤| π 1 (G …
G _ Q _p GQ p splits after a tamely ramified extension and p\not ∣| π _1 (G^ der)| p∤| π 1 (G …
The prismatic realization functor for Shimura varieties of abelian type
N Imai, H Kato, A Youcis - arXiv preprint arXiv:2310.08472, 2023 - arxiv.org
For the integral canonical model $\mathscr {S} _ {\mathsf {K}^ p} $ of a Shimura variety
$\mathrm {Sh} _ {\mathsf {K} _0\mathsf {K}^ p}(\mathbf {G},\mathbf {X}) $ of abelian type at …
$\mathrm {Sh} _ {\mathsf {K} _0\mathsf {K}^ p}(\mathbf {G},\mathbf {X}) $ of abelian type at …
Rapoport–Zink spaces of Hodge type
W Kim - Forum of Mathematics, Sigma, 2018 - cambridge.org
RAPOPORT–ZINK SPACES OF HODGE TYPE Page 1 Forum of Mathematics, Sigma (2018),
Vol. 6, e8, 110 pages doi:10.1017/fms.2018.6 1 RAPOPORT–ZINK SPACES OF HODGE …
Vol. 6, e8, 110 pages doi:10.1017/fms.2018.6 1 RAPOPORT–ZINK SPACES OF HODGE …
Regular rings and perfect (oid) algebras
B Bhatt, SB Iyengar, L Ma - Communications in Algebra, 2019 - Taylor & Francis
We prove ap-adic analog of Kunz's theorem: ap-adically complete noetherian ring is regular
exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a …
exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a …
Deformation theory for prismatic -displays
K Ito - arXiv preprint arXiv:2306.05361, 2023 - arxiv.org
For a smooth affine group scheme $ G $ over the ring of $ p $-adic integers and a
cocharacter $\mu $ of $ G $, we develop the deformation theory for $ G $-$\mu $-displays …
cocharacter $\mu $ of $ G $, we develop the deformation theory for $ G $-$\mu $-displays …
Prismatic -displays and descent theory
K Ito - arXiv preprint arXiv:2303.15814, 2023 - arxiv.org
For a smooth affine group scheme $ G $ over the ring of $ p $-adic integers $\mathbb {Z} _p
$ and a cocharacter $\mu $ of $ G $, we study $ G $-$\mu $-displays over the prismatic site …
$ and a cocharacter $\mu $ of $ G $, we study $ G $-$\mu $-displays over the prismatic site …