scholarly journals Differential forms on log canonical spaces in positive characteristic

2021 ◽  
Author(s):  
Patrick Graf
Keyword(s):  
Positive Characteristic ◽  
Differential Forms ◽  
Log Canonical

scholarly journals Extension theorems for differential forms and Bogomolov–Sommese vanishing on log canonical varieties

2009 ◽  
Vol 146 (1) ◽  
pp. 193-219 ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Sándor J. Kovács
Keyword(s):  
Differential Forms ◽  
Natural Generalization ◽  
Resolution Of Singularities ◽  
Vanishing Theorem ◽  
Exceptional Set ◽  
Extension Theorems ◽  
Normal Variety ◽  
Log Canonical ◽  
Smooth Locus

AbstractGiven a normal variety Z, a p-form σ defined on the smooth locus of Z and a resolution of singularities $\pi : \widetilde {Z} \to Z$, we study the problem of extending the pull-back π*(σ) over the π-exceptional set $E \subset \widetilde {Z}$. For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along E. As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov–Sommese vanishing theorem to log canonical threefold pairs follows.

scholarly journals Minimal Models and Abundance for Positive Characteristic Log Surfaces

2014 ◽  
Vol 216 ◽  
pp. 1-70 ◽  
Author(s):  
Hiromu Tanaka
Keyword(s):  
Finite Field ◽  
Minimal Model ◽  
Positive Characteristic ◽  
Algebraic Closure ◽  
Model Program ◽  
Minimal Models ◽  
Base Field ◽  
Singular Surfaces ◽  
Minimal Model Program ◽  
Log Canonical

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

scholarly journals Cohomological Invariants in Positive Characteristic

2021 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Positive Characteristic ◽  
Differential Forms ◽  
Symmetric Groups ◽  
Characteristic P ◽  
Motivic Cohomology ◽  
Cohomological Invariants ◽  
Group Schemes ◽  
Characteristic 2 ◽  
Theory Of Fields ◽  
Mod P

Abstract We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are invariants of $G$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $p$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $p$ Milnor K-theory of fields.

scholarly journals Differential forms on log canonical spaces

2011 ◽  
Vol 114 (1) ◽  
pp. 87-169 ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Sándor J Kovács ◽  
Thomas Peternell
Keyword(s):  
Differential Forms ◽  
Log Canonical

scholarly journals Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field

2017 ◽  
Vol 28 (05) ◽  
pp. 1750030 ◽  
Author(s):  
Hiromu Tanaka
Keyword(s):  
Finite Field ◽  
Positive Characteristic ◽  
Ample Divisor ◽  
Perfect Field ◽  
Log Canonical ◽  
Canonical Pair ◽  
Field Of Positive Characteristic

Let [Formula: see text] be an [Formula: see text]-finite field containing an infinite perfect field of positive characteristic. Let [Formula: see text] be a projective log canonical pair over [Formula: see text]. In this note, we show that, for a semi-ample divisor [Formula: see text] on [Formula: see text], there exists an effective [Formula: see text]-divisor [Formula: see text] such that [Formula: see text] is log canonical if there exists a log resolution of [Formula: see text].

scholarly journals Minimal Models and Abundance for Positive Characteristic Log Surfaces

2014 ◽  
Vol 216 ◽  
pp. 1-70 ◽  
Author(s):  
Hiromu Tanaka
Keyword(s):  
Finite Field ◽  
Minimal Model ◽  
Positive Characteristic ◽  
Algebraic Closure ◽  
Model Program ◽  
Minimal Models ◽  
Base Field ◽  
Singular Surfaces ◽  
Minimal Model Program ◽  
Log Canonical

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

scholarly journals Minimal model program for log canonical threefolds in positive characteristic

2020 ◽  
Vol 27 (4) ◽  
pp. 1003-1054
Author(s):  
Kenta Hashizume ◽  
Yusuke Nakamura ◽  
Hiromu Tanaka
Keyword(s):  
Minimal Model ◽  
Positive Characteristic ◽  
Model Program ◽  
Minimal Model Program ◽  
Log Canonical
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