This paper consists of two parts: in the first, we use the deformation theory of twisted sheaves on stacks to generalize results of de Jong and Saltman on the period-index problem for the Brauer group, yielding various new cases of the standard conjecture. In the second part, we use the geometric techniques of the first part to relate the Hasse principle for certain smooth projective geometrica...

Since numerical error is the source of non-robustness, it is natural to try to improve upon the standard floating point arithmetic. Can we improve on the conventional floating point arithmetic, which has already reached a highly optimal design under the IEEE Standard? More generally, what techniques are available in the FP mode of computation? In conventional floating point systems, the number ...

Throughout this presentation I have chosen to use a symbolic matrix notation. This choice was not made lightly. I am a strong advocate of index notation, when appropriate. For example, index notation greatly simplifies the presentation and manipulation of differential geometry. As a rule-of-thumb, if your work is going to primarily involve differentiation with respect to the spatial coordinates...

Let K be a complete discretely valued field with perfect residue field k. Assuming upper bounds on the relation between period and index for WC-groups over k, we deduce corresponding upper bounds on the relation between period and index for WC-groups over K. Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. ...

We describe an algebra of meromorphic functions on the Siegel domain genus two which contains modular forms for arithmetic index six subgroup symplectic group, is closed under three canonical derivations domain. The main ingredients our study are moduli enhanced curves, Gauss-Manin connection and vector fields living such spaces.

This paper presents an analytical view of variance reduction by control variate technique for pricing arithmetic Asian options as a financial derivatives. In this paper, the effect of correlation between two random variables is shown. We propose an efficient method for choose suitable control in pricing arithmetic Asian options based on the control variates (CV). The numerical experiment shows ...