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Similar Journals
 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 0      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [374 journals]
• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$A_{\text{inf}}$ ++++++++++++ ++++++++ ++++-cohomology+in+the+semistable+case&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2019&rft.volume=155&rft.spage=2039&rft.epage=2128&rft.aulast=Česnavičius&rft.aufirst=Kęstutis&rft.au=Kęstutis+Česnavičius&rft.au=Teruhisa+Koshikawa&rft_id=info:doi/10.1112/S0010437X1800790X">The $A_{\text{inf}}$ -cohomology in the semistable case
• Authors: Kęstutis Česnavičius; Teruhisa Koshikawa
Pages: 2039 - 2128
Abstract: For a proper, smooth scheme $X$ over a $p$ -adic field $K$ , we show that any proper, flat, semistable ${\mathcal{O}}_{K}$ -model ${\mathcal{X}}$ of $X$ whose logarithmic de Rham cohomology is torsion free determines the same ${\mathcal{O}}_{K}$ -lattice inside $H_{\text{dR}}^{i}(X/K)$ and, moreover, that this lattice is functorial in $X$ . For this, we extend the results of Bhatt–Morrow–Scholze on the construction and the analysis of an $A_{\text{inf}}$ -valued cohomology theory of $p$ -adic formal, proper, smooth
PubDate: 2019-11-01T00:00:00.000Z
DOI: 10.1112/S0010437X1800790X
Issue No: Vol. 155, No. 11 (2019)

• Zariski closures of images of algebraic subsets under the uniformization
map on finite-volume quotients of the complex unit ball
• Authors: Ngaiming Mok
Pages: 2129 - 2149
Abstract: We prove the analogue of the Ax–Lindemann–Weierstrass theorem for not necessarily arithmetic lattices of the automorphism group of the complex unit ball $\mathbb{B}^{n}$ using methods of several complex variables, algebraic geometry and Kähler geometry. Consider a torsion-free lattice $\unicode[STIX]{x1D6E4}\,\subset \,\text{Aut}(\mathbb{B}^{n})$ and the associated uniformization map $\unicode[STIX]{x1D70B}:\mathbb{B}^{n}\rightarrow \mathbb{B}^{n}/\unicode[STIX]{x1D6E4}=:X_{\unicode[STIX]{x1D6E4}}$ . Given an algebraic subset $S\,\subset \,\mathbb{B}^{n}$ and writing $Z$ for the Zariski closure of $\unicode[STIX]{x1D70B}(S)$ in $X_{\unicode[STIX]{x1D6E4}}$ (which is equipped with a canonical quasi-projective structure), in some precise sense we realize $Z$ as a variety uniruled by images of algebraic subsets under the uniformization map, and study the asymptotic geometry of an irreducible component $\widetilde{Z}$ of $\unicode[STIX]{x1D70B}^{-1}(Z)$ as
PubDate: 2019-11-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007577
Issue No: Vol. 155, No. 11 (2019)

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