Related papers: An obstruction to lifting to characteristic $0$

To an arbitrary variety over a field of characteristic zero, we associate a complex of Chow motives, which is, up to homotopy, unique and bounded. We deduce that any variety has a natural Euler characteristic in the Grothendieck group of…

We define a homomorphism from (a certain extension of) the fundamental group of the Hamiltonian automorphism group of a symplectic manifold to the group of invertibles in its quantum cohomology ring. The manifold must satify a technical…

We show that for any integer n and any field k of characteristic different from 2 there are at most finitely many isomorphism classes of quadratic morphisms from the projective line over k to itself with a finite postcritical orbit of size…

The finite monodromy groups of abelian varieties over number fields have been introduced by Grothendieck. They represent the local obstruction to semi-stable reduction. In this paper we prove a criteria for finite groups to be realized as…

A torsor under a k-group scheme G on a variety X over a number field k imposes a descent obstruction against the existence of rational points on X. We discuss the finite descent obstruction, that is for all such torsors under finite…

We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We…

Let $f\colon Y \to X$ be a proper flat morphism of locally noetherian schemes. Then, the locus in $X$ over which $f$ is smooth is stable under generization. We prove that under suitable assumptions on the formal fibers of $X$, the same…

We realize a graded variant $K_0(Var_k^{dim})$ of the Grothendieck ring of varieties as a quadratic extension of the subring $K_0(Var_k^{sp})$ spanned by classes of smooth and proper varieties. As such, there exists a natural involution…

The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…

Given a Noetherian formal scheme $\hat X$ over ${\rm Spf}(R)$, where $R$ is a complete DVR, we first prove a theorem of meromorphic descent along a possibly infinite cover of $\hat{X}$. Using this we construct a specialization functor from…

We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that…

We prove that a certain class of open homomorphisms between Galois groups of function fields of curves over finite fields arise from embeddings between the function fields.

We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety by a finite group of order prime to the…

Let $E:y^2=(x-e_1)(x-e_2)(x-e_3)$ be a nonconstant elliptic curve over $\mathbb{Q}(t)$, where $e_j\in \mathbb{Z}[t]$. We describe a method for finding a specialization $t\mapsto t_0\in\mathbb{Q}$ such that the specialization homomorphism is…

We prove that all endo-$p$-permutation modules for a finite group are liftable from characteristic $p>0$ to characteristic $0$.

The main purpose of this paper is to study cohomology and develop a deformation theory of restricted Lie algebras in positive characteristic $p>0$. In the case $p\geq3$, it is shown that the deformations of restricted Lie algebras are…

Let $G$ be a connected semi-simple group defined over and algebraically closed field, $T$ a fixed Cartan, $B$ a fixed Borel containing $T$, $S$ a set of simple reflections associated to the simple positive roots corresponding to $(T,B)$,…

Special covers are metacyclic covers of the projective line, with Galois group of order pm, which have a specific type of bad reduction to characteristic p. Such covers arise in the study of the arithmetic of Galois covers of the projective…

We introduce the notion of Grothendieck heaps for unpointed Waldhausen categories and unpointed stable $\infty$-categories. This allows an extension of the studies of $\mathrm{K}_0$ to the homotopy category of unpointed topological spaces.

Given a small simplicial category $\C$ whose underlying ordinary category is equipped with a Grothendieck topology $\tau$, we construct a model structure on the category of simplicially enriched presheaves on $\C$ where the weak…