We argue for finiteness of flux vacua around type IIB CY singularities by computing their gauge theory duals. This leads us to propose a geometric transition where the compact 3-cycles support both RR and NS flux, while the open string side contains 5-brane bound states. By a suitable combination of S duality and symplectic transformations, both sides are shown to have the same IR physics. The ...

We introduce the notion of wild partition to describe in combinatorial language an important situation in the theory of p-adic fields. For Q a power of p, we get a sequence of numbers λQ,n counting the number of certain wild partitions of n. We give an explicit formula for the corresponding generating function ΛQ(x) = ∑ λQ,nx and use it to show that λ Q,n tends to Q 1/(p−1). We apply this asymp...

Suppose X is a smooth projective scheme of finite type over a field K, E is a locally free OX -bimodule of rank 2, A is the non-commutative symmetric algebra generated by E and ProjA is the corresponding non-commutative P -bundle. We use the properties of the internal Hom functor HomGrA(−,−) to prove versions of Serre finiteness and Serre vanishing for ProjA. As a corollary to Serre finiteness,...

In this paper we give an elementary proof of certain finiteness results about affine Kac-Moody groups over a local non-archimedian field K. Our results imply those proven earlier in [5],[4] and [16] using either algebraic geometry or a Kac-Moody version of the Bruhat-Tits building. The above finiteness results allow one to formulate an affine version of the GindikinKarpelevich formula, which co...

Let T be a complete first order theory in a language L satisfying uniform finiteness and let TP be the model companion of T in an expanded language LP with a new unary predicate P . We show that: TP satisfies uniform finiteness; if T is an expansion of the theory of dense linear order then every cut definable in a model M of TP is definable in M L; and, if T is an expansion of the theory dense ...

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, a...

This paper is concerned with the question of when the crossed product of an AF algebra by an action of Z is itself AF embeddable. It is well known that quasidiagonality and stable finiteness are hereditary properties. That is, if A and B are C-algebras with A ⊂ B and B has either of these properties, then so does A. Since AF algebras enjoy both of these properties we have that quasidiagonality ...

We present a method for deciding when a regular abelian cover of a finite CWcomplex has finite Betti numbers. To start with, we describe a natural parameter space for all regular covers of a finite CW-complex X, with group of deck transformations a fixed abelian group A, which in the case of free abelian covers of rank r coincides with the Grassmanian of r-planes in H1(X,Q). Inside this paramet...

We introduce the notion of a Schur-finite element in a λ-ring. Since the beginning of algebraic K-theory in [G57], the splitting principle has proven invaluable for working with λ-operations. Unfortunately, this principle does not seem to hold in some recent applications, such as the K-theory of motives. The main goal of this paper is to introduce the subring of Schur-finite elements of any λ-r...

We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C, such that i) C lies in the hyperelliptic locus and ii) C is generated by an abelian differential with two zeros of order g − 1. We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.