Local-global principles for etale cohomology (10rit149)


David Harbater (University of Pennsylvania)

Julia Hartmann (University of Pennsylvania)

(University of Pennsylvania)


The "Local-global principles for etale cohomology" workshop will be hosted at The Banff International Research Station.

Our project uses patching to obtain local-global principles in cohomology. Both of these notions concern studying an object by doing so locally. In the case of patching, a global object can be constructed by doing so locally and indicating how the parts fit together. In the case of local-global principles, whether an object exists globally is determined by whether it exists locally. Through the application of patching to the study of local-global principles, we are able to obtain results about symmetries of mathematical objects; and from that we can obtain applications to solutions to quadratic polynomials in several variables and to certain algebraic systems in which multiplication is associative. In our proposed Research in Teams, our goal is to extend this approach to obtain new local-global principles that concern the deeper structure of algebraic systems, and that would have applications even to some systems where the associative law does not hold.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).