Related papers: Mittag-Leffler modules and variants on intersectio…

We present certain new properties about the intersection numbers on moduli spaces of curves $\bar{\sM}_{g,n}$, including a simple explicit formula of $n$-point functions and several new identities of intersection numbers. In particular we…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Let $(A,\m)$ be a Noetherian local ring, let $M$ be a finitely generated \CM $A$-module of dimension $r \geq 2$ and let $I$ be an ideal of definition for $M$. Set $L^I(M) = \bigoplus_{n\geq 0}M/I^{n+1}M$. In part one of this paper we showed…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12.…

In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a…

The theory of singularities defined by Frobenius has been extensively developed for $F$-finite rings and for rings that are essentially of finite type over excellent local rings. However, important classes of non-local excellent rings, such…

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

We generalize the work of Ohta on the congruence modules attached to elliptic Eisenstein series to the setting of Hilbert modular forms. Our work involves three parts. In the first part, we construct Eisenstein series adelically and compute…

Classical definitions of locally complete intersection (l.c.i.) homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this paper is meaningful for homomorphisms phi :…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over…

Let u be a local homomorphism of noetherian local rings forming part of a commutative square vf=gu. We give some conditions on the square which imply that u is formally smooth. This result encapsulates a variety of (apparently unrelated)…

Let $R$ be an associative ring with unit. Given an $R$-module $M$, we can associate the following covariant functor from the category of $R$-algebras to the category of abelian groups: $S\mapsto M\otimes_R S$. With the corresponding notion…

Obstruction flatness of a strongly pseudoconvex hypersurface $\Sigma$ in a complex manifold refers to the property that any (local) K\"ahler-Einstein metric on the pseudoconvex side of $\Sigma$, complete up to $\Sigma$, has a potential…

We investigate the relation between partial silting modules, Gabriel topologies, and ring epimorphisms, with a particular emphasis on commutative rings. We show that a ring epimorphism of commutative rings is flat if and only if it is a…

Let G be a Lie group endowed with a bi-invariant pseudo-Riemannian metric. Then the moduli space of flat connections on a principal G-bundle, P\to \Sigma, over a compact oriented surface, \Sigma, carries a Poisson structure. If we…

We shall construct a natural Higgs bundle structure on the complexified K\"ahler cone of a compact K\"ahler manifold, which can be seen as an analogy of the classical Higgs bundle structure associated to a variation of Hodge structure. In…

We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…

Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely one where finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence.…