American Institute of Mathematics, Palo Alto, California
Dinakar Ramakrishnan and Wayne Raskind
This workshop, sponsored by AIM and the NSF, will be devoted to the conjecture of Tate which characterizes the cohomology classes of algebraic cycles on an algebraic varietyX over a field k that is finitely generated over the prime field in terms of the fixed space of even-dimensional l-adic etale cohomology under the action of the absolute Galois group G of k. Here l is a prime number different from the characteristic of k. This conjecture is an arithmetic analogue of the Hodge conjecture for varieties over the complex numbers. While the Tate conjecture is over 40 years old and has been verified in many cases, we still lack a true understanding of why it should hold in general. The main purpose of the workshop is to bring experts in various aspects of the field together to synthesize the known methods and then develop strategies for understanding and attacking the conjecture in a more general way.
The main topics on which we will focus include:
The organizers hope that participants might be willing to share any vague and/or unpublished ideas they might have about the Tate conjecture in the working sessions, and that the atmosphere and format of AIM workshops will be conducive to significant progress being achieved during or shortly after the meeting.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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