A non-Archimedean analogue of the Hodge-D-conjecture for products of elliptic curves

In this paper we show that the map % \partial:CH^2(E_1 \times E_2,1)\otimes \Q \longrightarrow PCH^1(\XX_v) % is surjective, where $E_1$ and $E_2$ are two non-isogenous semistable elliptic curves over a local field, $CH^2(E_1 \times E_2,1)$ is one of Bloch's higher Chow groups and PCH^1(\XX_v) is a certain subquotient of a Chow group of the special fibre \XX_{v} of a semi-stable model \XX of $E_1 \times E_2$. On one hand, this can be viewed as a non-Archimedean analogue of the Hodge-\D-conjecture of Beilinson - which is known to be true in this case by the work of Chen and Lewis \cite{lech}, and on the other, an analogue of the works of Spei{\ss} \cite{spie}, Mildenhall \cite{mild} and Flach \cite{flac} in the case when the elliptic curves have split multiplicative reduction.Comment: 13 pages. To appear in the Journal of Algebraic Geometr

Visual Information Retrieval in Digital Libraries

The emergence of information highways and multimedia computing has resulted in redefining the concept of libraries. It is widely believed that in the next few years, a significant portion of information in libraries will be in the form of multimedia electronic documents. Many approaches are being proposed for storing, retrieving, assimilating, harvesting, and prospecting information from these multimedia documents. Digital libraries are expected to allow users to access information independent of the locations and types of data sources and will provide a unified picture of information. In this paper, we discuss requirements of these emerging information systems and present query methods and data models for these systems. Finally, we briefly present a few examples of approaches that provide a preview of how things will be done in the digital libraries in the near future.published or submitted for publicatio