We study deformations of associative submanifolds Y 3 ⊂ M of a G2 manifold M . We show that the deformation space can be perturbed to be smooth, and it can be made compact and zero dimensional by constraining it with an additional equation. This allows us to associate local invariants to associative submanifolds of M . The local equations at each associative Y are restrictions of a global equat...

The work of Dipper and James on Iwahori-Hecke algebras associated with the finite Weyl groups of type An has shown that these algebras behave in many ways like group algebras of finite groups. Moreover, there are “generic” features in the modular representation theory of these algebras which, at present, can only be verified in examples by explicit computations. This paper arose from an attempt...

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals. Let H be a complex infinite-dimensional separable Hilbert space, which is of course unique up to isomorphism. Let B(H) be the Banach algebra of bounded linear operators on H, and let C(H) be the clo...

We prove new height inequalities for determinantal ideals in a regular local ring, or more generally in a local ring of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns. Introduction. Let φ be a map of vector bundles on a variety X. A wellknown theorem of Eagon and Northcott [EN] gives an upper bound for the codimension of the locus where φ has rank ≤ s...

We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of a...

According to several classical results by Bézout, Sylvester, Cayley, and others, the classical discriminant Dn of degree n polynomials may be expressed as the determinant of a matrix whose entries are much simpler polynomials in the coefficients of f . However, all of the determinantal formulae for Dn appearing in the classical literature are equivalent in the sense that the cokernels of their ...

Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...

C. Deninger produced a unified description of the local factors at arithmetic infinity and at the finite places where the local Frobenius acts semi-simply, in the form of a Ray–Singer determinant of a “logarithm of Frobenius” Φ on an infinite dimensional vector space (the archimedean cohomology H · ar(X) at the archimedean places, cf. [11]). The first author gave a cohomological interpretation ...

Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...