HOMOQCSSTACKS (293890)

  https://cordis.europa.eu/project/id/293890

  FP7 (2007-2013)

  Homotopy theory of quasi-coherent sheaves on stacks

  Marie-Curie Action: "Career Integration Grants" (FP7-PEOPLE-2011-CIG)

  topology  ·  geometry  ·  algebraic geometry

  2012-01-15 Start Date (YY-MM-DD)

  2017-06-05 End Date (YY-MM-DD)

  € 100,000 Total Cost

  Description

In the last decade there has been a growing interconnection between algebraic geometry and homotopy theory. This project is part of that exciting development. The primary researcher has developed a homotopy theoretic approach to the theory of stacks. As part of this project the PI will apply this approach to the study of quasi-coherent sheaves on stacks and questions of representability by algebraic stacks. The PI plans to prove a series of structural results about the categories of quasi-coherent sheaves, including existence of pushforward and pullback functors, internal Hom, completions, and localizations, for a very general class of stacks. These results can then be applied to understand the structure of the categories of quasi-coherent sheaves and should have important applications in algebra and topology. In particular, the PI will show how these statements can be applied to the moduli stack of formal groups leading to new results in stable homotopy theory.

  Complicit Organisations

1 Israeli organisation participates in HOMOQCSSTACKS.