Related papers: Duals and pullbacks of normed modules

In this note we study the weak topology on paired modules over a (not necessarily commutative) ground ring. Over QF rings we are able to recover most of the well known properties of this topology in the case of commutative base fields. The…

We give a log-geometric description of the space of twisted canonical divisors constructed by Farkas--Pandharipande. In particular, we introduce the notion of a principal rubber $k$-log-canonical divisor, and we study its moduli space. It…

We conjecture that the "nilpotent points" of Calogero-Moser space for reflection groups are parametrised naturally by the two-sided cells of the group with unequal parameters. The nilpotent points correspond to blocks of restricted…

Motivated by recent developments on calculus in metric measure spaces $(X,\mathsf d,\mathfrak m)$, we prove a general duality principle between Fuglede's notion of $p$-modulus for families of finite Borel measures in $(X,\mathsf d)$ and…

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…

Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~M\"oller, from the viewpoint of flat and complex geometry, for the purpose of compactifying moduli spaces of curves together with a…

We separate the local diameter two property from the diameter two property and their weak-star counterparts from each other in spaces of Lipschitz functions. We characterise the $w^*$-LD$2$P, the $w^*$-D$2$P, the LD$2$P, and the SD$2$P in…

The naive blow-up algebras developed by Keeler-Rogalski-Stafford, after examples of Rogalski, are the first known class of connected graded algebras that are noetherian but not strongly noetherian. This failure of the strong noetherian…

We study the so-called K-positive linear maps from B(L) into B(H) for finite dimensional Hilbert spaces L and H and give characterizations of the dual cone of the cone of K-positive maps. Applications are given to decomposable maps and…

A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra…

We define a type of modulus $\operatorname{dMod}_p$ for Lipschitz surfaces based on $L^p$-integrable measurable differential forms, generalizing the vector modulus of Aikawa and Ohtsuka. We show that this modulus satisfies a homological…

To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule…

This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of the Lyapunov exponent of the shift of the continued fraction,…

This paper explores the implications of blocking duality---pioneered by Fulkerson et al.---in the context of $p$-modulus on networks. Fulkerson's blocking duality is an analogue on networks to the method of conjugate families of curves in…

For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential…

We describe moduli spaces of logarithmic rank $2$ connections on elliptic curves with $n \geq 1$ poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze…

The notion of $P$-algebra due to Margolis, building on work of Moore and Peterson, was motivated by the case of the Steenrod algebra at a prime and its modules. We develop aspects of this theory further, focusing especially on coherent…

Let $H$ be a weak Hopf algebra with a bijective antipode and $A$ an $H$-comodule Poisson algebra. In this paper, we mainly generalize the fundamental theorem of Poisson Hopf modules to the case of weak Hopf algebras. Besides we will deduce…

A well-known result by Larson and Sweedler shows that integrals on a Hopf algebra can be obtained by applying the Structure Theorem for Hopf modules to the rational part of its linear dual. This fact can be rephrased by saying that taking…

This is the second part of the article [math.KT/0408094]. In the first paper, we used the underlying coalgebra structure to develop a cyclic theory. In this paper we define a dual theory by using the algebra structure. We define a cyclic…