We apply constructions from equivariant topology to Benson-Carlson resolutions and hence prove in (2.1) that the group cohomology ring of a nite group enjoys remarkable duality properties based on its global geometry. This recovers and generalizes the result of Benson-Carlson stating that a Cohen-Macaulay cohomology ring is automatically Gorenstein. We give an alternative approach to Tate cohom...

The purpose of this note is to complement part of a theorem from the remarkable paper of Fontaine and Mazur on geometric Galois representations [5]. Fix a prime p, and let K be a finite extension of the p-adic numbers Qp. Fix an algebraic closure K̄ of K and let G be the Galois group of K̄ over K. Fontaine’s theory [3] classifies various types of representations ρ : G→Aut(V) on finite-dimensional...

We introduce tropical corals, balanced trees in a half-space, and show that they correspond to holomorphic polygons capturing the product rule Lagrangian Floer theory for elliptic curve. then prove correspondence theorem equating counts of corals punctured log Gromov–Witten invariants Tate This implies homogeneous coordinate ring mirror curve is isomorphic degree-zero part symplectic cohomology...

The Tate is Britain's premier national art gallery and includes content from internationally-renowned artists such as Constable and Turner. Like most cultural heritage institutions, the Tate provides online access to a large amount of digitized material. Given the international importance of content provided by the Tate Gallery, multilingual access would seem an ideal way in which to increase a...

In this paper, we will implement a standard probabilistic method of computing bilinear pairings. We will compare its performance to a deterministic algorithm introduced in [5] to compute the squared Tate/Weil pairings which are claimed to be 20 percent faster than the standard method. All pairings will be evaluated over pairing-friendly ordinary elliptic curves of embedding degrees 8 and 10 and...

Feynman amplitudes, which play a central role in perturbative quantum field theory, are algebro-geometric periods associated to graphs. These periods have been investigated by Broadhurst and Kreimer (see [4] and the references cited there) and shown for many special graphs to be sums of multiple zeta values. On the other hand, Belkale and Brosnan have shown [2] that the related graph motives ar...

The bifunctional chelator and radiometal have been shown to have a direct effect on the pharmacokinetics of somatostatin receptor (SSTR)-targeted imaging agents. We evaluated three Y3-TATE analogues conjugated to NOTA-based chelators for radiolabeling with 64Cu and 68Ga for small-animal positron emission tomographic/computed tomograhic (PET/CT) imaging. Two commercially available NOTA analogues...

The Weil and Tate pairings have been used recently to build new schemes in cryptography. It is known that the Weil pairing takes longer than twice the running time of the Tate pairing. Hence it is necessary to develop more efficient implementations of the Tate pairing for the practical application of pairing based cryptosystems. In 2002, Barreto et al. and Galbraith et al. provided new algorith...

An object-oriented real t i m e sy s t ems conceptual modeling approach is described. In this approach, each object is specified by a n object type, consisting of supertypes (inheritance), component types (aggregation), attributes, operations, s tat ic constraints, and t imed temporal constraints. An object type specification def i nes a theory of a type of objects. In particular, t he s tat ic...