Related papers: Cube invariance of higher Chow groups with modulus

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of $(\alpha, \beta)$-derivation to $(\alpha, \beta)$-higher derivation and demonstrate that a filter of a hereditary…

Let $(\mathcal{K},\mathcal{O},k)$ be a $p$-modular system with $k$ algebraically closed, let $b$ be a block of the normal subgroup $H$ of $G$ having defect pointed group $Q_\delta$ in $H$ and $P_\gamma$ in $G$, and consider the block…

The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. This book explores a "linearization"…

We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the…

Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…

We prove that the mapping class group is not an $h$-cobordism invariant of high-dimensional manifolds by exhibiting $h$-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli…

We introduce equivariant Chow-Witt groups in order to define Chow-Witt groups of quotient stacks. We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new…

Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…

We determine the Chow ring (with Q-coefficients) of M_6 by showing that all Chow classes are tautological. In particular, all algebraic cohomology is tautological, and the natural map from Chow to cohomology is injective. To demonstrate the…

We study the noncommutative modular curve (which was already studied by Connes, Manin and Marcolli), and the space of geodesics on the usual modular curve, from the viewpoint of algebraic groups, linear algebra and class field theory. This…

In this article, we prove that induced modules of support $\tau$-tilting modules over blocks of finite groups satisfying inertial-invariant condition are also support $\tau$-tilting modules.

Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the…

We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…

Starting from ideas of Furuta, we develop a general formalism for the construction of cohomotopy invariants associated with a certain class of $S^1$-equivariant non-linear maps between Hilbert bundles. Applied to the Seiberg-Witten map,…

We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group…

We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…

We derive conjectures, called genus 1 Enumerative mirror symmetry for moduli spaces of Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm{SL}_r$-bundles to curve-counting invariants of moduli spaces of…

Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…

In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irreducible solutions from which we can build all the…

Title: Indecomposable Higher Chow Cycles on Low Dimensional Jacobians Authors: Alberto Collino Comments: AMS-TeX, 10 pages Subj-class: Algebraic Geometry MSC-class: 14C30 ;19E15 There is a basic indecomposable higher cycle K in Bloch's…