scholarly journals Basepoint-free Theorem of Reid–Fukuda Type for Quasi-log Schemes

2016 ◽  
Vol 52 (1) ◽  
pp. 63-81 ◽  
Author(s):  
Osamu Fujino
Keyword(s):  
Log Schemes

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 Monomorphisms in categories of log schemes

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

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.

scholarly journals Kato–Nakayama spaces, infinite root stacks and the profinite homotopy type of log schemes

2017 ◽  
Vol 21 (5) ◽  
pp. 3093-3158 ◽  
Author(s):  
David Carchedi ◽  
Sarah Scherotzke ◽  
Nicolò Sibilla ◽  
Mattia Talpo
Keyword(s):  
Homotopy Type ◽  
Log Schemes

scholarly journals Extending families of curves over log regular schemes

1999 ◽  
Vol 1999 (511) ◽  
pp. 43-71 ◽  
Author(s):  
Shinichi Mochizuki
Keyword(s):  
Toric Varieties ◽  
Extension Theorem ◽  
Regular Case ◽  
Natural Conditions ◽  
Stable Curves ◽  
Families Of Curves ◽  
Moduli Stack ◽  
Regular Scheme ◽  
Log Schemes

Abstract In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism satisfying certain conditions from the complement of a divisor with normal crossings in a regular scheme to a moduli stack of stable curves extends over the entire regular scheme. The proof uses the theory of “regular log schemes” — i.e., schemes with singularities like those of toric varieties – due to K. Kato ([12]). We then use this extension theorem to prove that under certain natural conditions any scheme which is a successive fibration of smooth hyperbolic curves may be compactified to a successive fibration of stable curves.

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