Comparison between rigid and crystalline syntomic cohomology for strictly semistable log schemes with boundary

2021 ◽  
Author(s):  
Veronika Ertl ◽  
Kazuki Yamada
Keyword(s):  
Log Schemes ◽  
Syntomic Cohomology

KUMMER COVERINGS AND SPECIALISATION

2021 ◽  
pp. 1-37
Author(s):  
Martin Olsson
Keyword(s):  
Local Ring ◽  
Fundamental Groups ◽  
Technical Result ◽  
Noetherian Local Ring ◽  
Log Schemes ◽  
Log Scheme

Abstract We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.

scholarly journals K-theory of log-schemes II: Log-syntomic K-theory

2012 ◽  
Vol 230 (4-6) ◽  
pp. 1646-1672 ◽  
Author(s):  
Wiesława Nizioł
Keyword(s):  
K Theory ◽  
Log Schemes

scholarly journals Logarithmically regular morphisms

2020 ◽  
Author(s):  
Sam Molcho ◽  
Michael Temkin
Keyword(s):  
Simple Criterion ◽  
Log Schemes ◽  
Log Scheme

AbstractWe consider the stack $${\mathcal {L}}og_{X}$$ L o g X parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via $${\mathcal {L}}og_{X}$$ L o g X , as defined by Olsson. We give a concrete combinatorial presentation of $${\mathcal {L}}og_{X}$$ L o g X , and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato’s chart criterion of logarithmic smoothness.

scholarly journals Syntomic cohomology and $p$-adic étale cohomology

1992 ◽  
Vol 44 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Kazuya Kato ◽  
William Messing
Keyword(s):  
Etale Cohomology ◽  
Étale Cohomology ◽  
Syntomic Cohomology

scholarly journals Monomorphisms in categories of log schemes

2015 ◽  
Vol 38 (2) ◽  
pp. 365-429
Author(s):  
Shinichi Mochizuki
Keyword(s):  
Log Schemes

scholarly journals Syntomic cohomology and Beilinson’s Tate conjecture for $K_2$

2012 ◽  
Vol 22 (3) ◽  
pp. 481-547 ◽  
Author(s):  
Masanori Asakura ◽  
Kanetomo Sato
Keyword(s):  
Tate Conjecture ◽  
Syntomic Cohomology

Notes on algebraic log stack

2016 ◽  
Vol 27 (10) ◽  
pp. 1650081 ◽  
Author(s):  
Junchao Shentu ◽  
Dong Wang
Keyword(s):  
Moduli Stacks ◽  
Log Schemes

Let [Formula: see text] be a stack over the category of fine log schemes. If [Formula: see text] has a representable fppf covering, then, it has enough compatible minimal objects. As a consequence, we prove the equivalence between two notions of log moduli stacks which appear in literatures. Also, we obtain several fundamental results of algebraic log stacks.

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