Related papers: Pseudo-effective classes and pushforwards

In this paper, we prove the holomorphic convexity of the covering of a complex projective {normal} variety $X$, which corresponds to the intersection of kernels of reductive representations $\rho:\pi_1(X)\to {\rm GL}_{N}(\mathbb{C})$,…

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

Let $H$ be a Hopf algebra over a field $k$, and $A$ an $H$-comodule algebra. The categories of comodules and relative Hopf modules are then Grothendieck categories with enough injectives. We study the derived functors of the associated Hom…

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected…

We define a class of morphisms between strict $\omega$-categories called discrete Conduch{\'e} $\omega$-functors that generalize discrete Conduch{\'e} functors between 1-categories and we study their properties related to polygraphs. The…

We show how to attach to any rigid analytic variety $V$ over a perfectoid space $P$ a rigid analytic motive over the Fargues-Fontaine curve $\mathcal{X}(P)$ functorially in $V$ and $P$. We combine this construction with the overconvergent…

We prove that the mod 2-cohomology algebras of real projective groups are formal. As a consequence we derive the Hopkins-Wickelgren formality and the strong Massey vanishing conjecture for a large class of fields.

The Lefschetz algebra $L^*(X)$ of a smooth complex projective variety $X$ is the subalgebra of the cohomology algebra of $X$ generated by divisor classes. We construct smooth complex projective varieties whose Lefschetz algebras do not…

We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms…

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$.…

For a smooth complex projective variety X defined over a number field, we have filtrations on the Chow groups depending of the choice of realizations. If the realization consists of mixed Hodge structure without any additional structure, we…

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…

Let $R$ be a ring and Ch($R$) the category of chain complexes of $R$-modules. We put an abelian model structure on Ch($R$) whose homotopy category is equivalent to $K(Proj)$, the homotopy category of all complexes of projectives. However,…

The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of…

We prove that under semismall smooth flops, smooth projective varieties have (non-canonically) isomorphic Chow motives with coefficients in any noetherian local ring $\Lambda$ by comparing the pushforward of the constant intersection…

We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…

The geometric models for the module category and derived category of any gentle algebra were introduced to realize the objects in module category and derived category by permissible curves and admissible curves respectively. The present…

Given a complex affine hypersurface with isolated singularity determined by a homogeneous polynomial, we identify the noncommutative Hodge structure on the periodic cyclic homology of its singularity category with the classical Hodge…

We prove a formula which compares intersection numbers of conormal varieties of two projective varieties and their dual varieties. When one of them is linear, we can recover the usual Plucker formula for the degree of the dual variety. The…