Related papers: On the structure of flat chains modulo $p$

This paper proves a result on the existence of finite flat scheme covers of Deligne-Mumford stacks. This result is used to prove that a large class of smooth Deligne-Mumford stacks with affine moduli space are quotient stacks, and in the…

Let G be a group acting isometrically with discrete orbits on a separable complete CAT(0)-space of bounded topological dimension. Under certain conditions, we give upper bounds for the Bredon cohomological dimension of G for the families of…

We prove the existence of tilting bundles on global quotient stacks that are produced by compatible finite group actions on flat families.

Let $X$ and $S$ be complex spaces with $X$ countable at infinity and $S$ reduced locally pure dimensional. Let $\pi:X\to S$ be an universally-$n$-equidimensional morphism (i.e open with constant pure $n$-dimensional fibers). If there is a…

Let $p$ be a prime. We study the structure of and the inclusion relations among the terms in the monomial lattice in the modular symmetric power representations of $\mathrm{GL}_2(\mathbb{F}_p)$. We also determine the structure of certain…

The groups of (linear) similarity and coincidence isometries of certain modules in d-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered. It is shown that the structure of the factor group of…

A ring $R$ is called left GF-closed, if the class of all Gorenstein flat left $R$-modules is closed under extensions. The class of left GF-closed rings includes strictly the one of right coherent rings and the one of rings of finite weak…

We study the stability of the Positive Mass Theorem using the Intrinsic Flat Distance. In particular we consider the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature and no…

Given a holomorphic self-map of complex projective space of degree larger than one, we prove that there exists a finite collection of totally invariant algebraic sets with the following property: given any positive closed (1,1)-current of…

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the…

In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the…

Motivated by the connection to 4d $\mathcal{N}=2$ theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne-Mumford moduli space of stable pointed…

Let $S$ be a closed, genus $g$ surface. The space of geodesic currents on $S$ encompasses the set of closed curves up to homotopy, as well as Teichm\"uller space, and many other spaces of structures on $S$. We show that one can define a…

Gives the most precise available description of the p-Frattini module for any p-perfect finite group G=G_0 (Thm. 2.8), and therefore of the groups G_{k,ab}, k \ge 0, from which we form the abelianized M(odular) T(ower). \S 4 includes a…

We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…

It is widely believed that the parity of the partition function $p(n)$ is ``random.'' Contrary to this expectation, in this note we prove the existence of infinitely many congruence relations modulo 4 among its values. For each square-free…

We give necessary and sufficient conditions for moduli spaces of semistable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL_n-Higgs bundles and the…

In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…

We summarize recent work on the classification of modular invariant partition functions that can be obtained with simple currents in theories with a center (Z_p)^k with p prime. New empirical results for other centers are also presented.…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…