Related papers: Schur finiteness and nilpotency

We provide a sufficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a Q-linear tensor category with a tensor functor to super vector…

We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the Conjectures of Beilinson, Bloch and Murre on the existence of a filtration on the Chow ring CH(X). We…

In this article we study the class of Schur-finite motives, that is, motives which are annihilated by a Schur functor. We compare this notion to a similar one due to Kimura. In particular, we show that the motive of any curve is…

Making use of the recent theory of noncommutative motives, we prove that Schur-finiteness in the setting of Voevodsky's mixed motives is invariant under homological projective duality. As an application, we show that the mixed motives of…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

For a smooth projective surface X the finite dimensionality of the Chow motive h(X), as conjectured by S.I Kimura, has several geometric consequences. For a complex surface of general type with p_g = 0 it is equivalent to Bloch's…

A finite group $G$ is called a Schur group if every $S$-ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of $\sym(G)$ that contains all right translations. We prove that every nonabelian nilpotent Schur group…

Let X be a smooth projective variety. Starting with a finite set of cycles on powers X^m of X, we consider the Q-vector subspaces of the Q-linear Chow groups of the X^m obtained by iterating the algebraic operations and pullback and push…

We study the construction of arXiv:2111.11217 [math:AG] in more detail, especially in the case of Schur-finite rigid $\otimes$-categories. This leads to some groundwork on the ideal structure of rigid additive and abelian…

Let $\mathcal{C}$ be an additive category. The nilpotent category $\mathrm{Nil} (\mathcal{C})$ of $\mathcal{C}$, consists of objects pairs $(X, x)$ with $X\in\mathcal{C}, x\in\mathrm{End}_{\mathcal{C}}(X)$ such that $x^n=0$ for some…

We associate a rational number $\chi(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $\chi$ is additive under disjoint union and it preserves products. Hence we consider…

We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be…

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…

For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is injective. We prove that Voisin's conjecture…

In this paper, for any Shimura datum $(G,\mathcal{D})$ satisfying reasonable conditions so that many interesting cases satisfy, we prove some finiteness theorems for any graded vector space consisting of automorphic forms on $\mathcal{D}$…

Let X=G/P be cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) We say a Schubert class [S] is Schur rigid if the only irreducible subvarieties Y of X with homology class…

Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\Rico:=\Ric-\frac{R}{n}g$$ is identically zero. In this short…

It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…

We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly, infinite-dimensional)…

Let $f: X \rightarrow C$ be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let $j: J \rightarrow C$ be the Jacobian fibration of $f$. In this paper, we prove that the Chow motives of…