12 citations · 53 across the 10 of their papers we have counts for
12 papers
The cone theorem for effective fourfold pairs in characteristic
Joe Waldron
Assuming the log resolution conjecture for all log pairs birational to , we prove the cone theorem for projective log canonical, -factorial fourfold pairs su…
Mori fibre spaces for -folds over imperfect fields
Joe Waldron
We prove that the LMMP works for projective threefolds over function fields of characteristic when the canonical divisor is not pseudo-effective. In the process we show that…
Purely Inseparable Galois theory I: The Fundamental Theorem
Lukas Brantner, Joe Waldron
We construct a Galois correspondence for finite purely inseparable field extensions , generalising a classical result of Jacobson for extensions of exponent one (where $x^p \i…
Connectedness principle for -folds in characteristic
Stefano Filipazzi, Joe Waldron
A conjecture, known as the Shokurov-Kollár connectedness principle, predicts the following. Let be a pair, and let be a contraction with $-(K_X +…
On the log minimal model program for -folds over imperfect fields of characteristic
Omprokash Das, Joe Waldron
We prove that many of the results of the LMMP hold for -folds over fields of characteristic which are not necessarily perfect. In particular, the existence of flips, the c…
An analog of adjoint ideals and PLT singularities in mixed characteristic
Linquan Ma, Karl Schwede, Kevin Tucker +2
We use the framework of perfectoid big Cohen-Macaulay algebras to define a class of singularities for pairs in mixed characteristic, which we call purely BCM-regular singularities,…
Structure of geometrically non-reduced varieties
Lena Ji, Joe Waldron
We prove a structural result for geometrically non-reduced varieties and give applications to Fano varieties. For example, we show that if is the generic fibre of a Mori fibre…
Singularities of General Fibers and the LMMP
Zsolt Patakfalvi, Joe Waldron
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to…
On the Abundance Problem for -folds in characteristic
Omprokash Das, Joe Waldron
In this article we prove two cases of the abundance conjecture for -folds in characteristic : is KLT and , and is KLT, $K_X\eq…
The LMMP for log canonical 3-folds in char
Joe Waldron
We prove that one can run the log minimal model program for log canonical -fold pairs in characteristic . In particular we prove the Cone Theorem, Contraction Theorem, the…
Finite generation of the log canonical ring for 3-folds in char
Joe Waldron
We prove that the log canonical ring of a klt pair of dimension with -boundary over an algebraically closed field of characteristic is finitely generated. In…
Existence of Mori fibre spaces for 3-folds in char
Caucher Birkar, Joe Waldron
We prove the following results for projective klt pairs of dimension over an algebraically closed field of char : the cone theorem, the base point free theorem, the contra…