31 citations · 84 across the 26 of their papers we have counts for
31 papers · 1 filter
Symmetric Differentials on K3 Surfaces
Frank Gounelas, Christian Liedtke
We prove that a K3 surface over an algebraically closed field admits a nonzero global symmetric differential of positive degree if and only if the characteristic is , and it i…
Non-commutative resolutions of linearly reductive quotient singularities
Christian Liedtke, Takehiko Yasuda
We prove existence of non-commutative crepant resolutions (in the sense of van den Bergh) of quotient singularities by finite and linearly reductive group schemes in positive chara…
A McKay Correspondence in Positive Characteristic
Christian Liedtke
We establish a McKay correspondence for finite and linearly reductive subgroup schemes of in positive characteristic. As an application, we obtain a McKay correspon…
Torsors over the Rational Double Points in Characteristic
Christian Liedtke, Gebhard Martin, Yuya Matsumoto
We study torsors under finite group schemes over the punctured spectrum of a singularity in positive characteristic. We show that the Dieudonné module of the (loc,loc)-par…
Linearly Reductive Quotient Singularities
Christian Liedtke, Gebhard Martin, Yuya Matsumoto
We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known pro…
Rational curves on lattice-polarised K3 surfaces
Xi Chen, Frank Gounelas, Christian Liedtke
Fix a K3 lattice of rank two and a big and nef divisor that is positive enough. We prove that the generic -polarised K3 surface has an integral nodal rational curve…
Curves on K3 surfaces
Xi Chen, Frank Gounelas, Christian Liedtke
We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive…
p-adic Tate conjectures and abeloid varieties
Oliver Gregory, Christian Liedtke
We explore Tate-type conjectures over -adic fields. We study a conjecture of Raskind that predicts the surjectivity of $$ ({\rm NS}(X_{\bar{K}}) \otimes_{\mathbb{Z}}\mathbb{Q}_p…
Good reduction of K3 Surfaces in equicharacteristic p
Bruno Chiarellotto, Christopher Lazda, Christian Liedtke
We show that for smooth and proper varieties over local fields with no non-trivial vector fields, good reduction descends over purely inseparable extensions. We use this to extend…
Deformations of rational curves in positive characteristic
Kazuhiro Ito, Tetsushi Ito, Christian Liedtke
We study deformations of rational curves and their singularities in positive characteristic. We use this to prove that if a smooth and proper surface in positive characteristic …
A Néron-Ogg-Shafarevich criterion for K3 surfaces
Bruno Chiarellotto, Christopher Lazda, Christian Liedtke
The naive analogue of the Néron-Ogg-Shafarevich criterion is false for K3 surfaces, that is, there exist K3 surfaces over Henselian, discretely valued fields , with unramified $…
The Picard Rank of an Enriques Surface
Christian Liedtke
In this note, we use crystalline methods and the Tate-conjecture to give a short proof that the Picard rank of an Enriques surface is equal to its second Betti number.
Morphisms to Brauer-Severi Varieties, with Applications to Del Pezzo Surfaces
Christian Liedtke
We classify morphisms from proper varieties to Brauer-Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated…
Good Reduction of K3 Surfaces
Christian Liedtke, Yuya Matsumoto
Let be the field of fractions of a local Henselian DVR with perfect residue field. Assuming potential semi-stable reduction, we show that an unramified Galois-action on second…
Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem
Christian Liedtke
We survey crystalline cohomology, crystals, and formal group laws with an emphasis on geometry. We apply these concepts to K3 surfaces, and especially to supersingular K3 surfaces.…
Supersingular K3 Surfaces are Unirational
Christian Liedtke
We show that supersingular K3 surfaces in characteristic are related sequences of very special correspondences. This is not enough to conclude that they are unirational. A…
On the Birational Nature of Lifting
Christian Liedtke, Matthew Satriano
Let and be proper birational varieties, say with only rational double points over a perfect field of positive characteristic. If lifts to , is it true that…
Rational Curves on K3 Surfaces
Jun Li, Christian Liedtke
We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spac…
Arithmetic Moduli and Lifting of Enriques Surfaces
Christian Liedtke
We construct the moduli space of Enriques surfaces in positive characteristic and eventually over the integers, and determine its local and global structure. As an application, we…
The Canonical Map and Horikawa Surfaces in Positive Characteristic
Christian Liedtke
We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even…
Elliptic K3 surfaces with p^n-torsion sections
Hiroyuki Ito, Christian Liedtke
We classify elliptic K3 surfaces in characteristic with -torsion sections. For we verify conjectures of Artin and Shioda, compute the heights of their formal Br…
Algebraic Surfaces in Positive Characteristic
Christian Liedtke
These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in charact…
Birational modifications of surfaces via unprojections
Christian Liedtke, Stavros Argyrios Papadakis
We describe elementary transformations between minimal models of rational surfaces in terms of unprojections. These do not fit into the framework of Kustin-Miller unprojections as…
The p-torsion subgroup scheme of an elliptic curve
Christian Liedtke
Let be a field of positive characteristic . Question: Does every twisted form of over occur as subgroup scheme of an elliptic curve over ? We show that this is…