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Details of Grant 

EPSRC Reference: EP/J013064/1
Title: Enriched motivic homotopy theory
Principal Investigator: Garkusha, Professor G
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: College of Science
Organisation: Swansea University
Scheme: Standard Research
Starts: 15 April 2012 Ends: 14 September 2012 Value (£): 22,213
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
The versatility of motivic homotopy theory and its associated range of cohomological techniques has made it an important branch of mathematics. Recently there have been several fundamental developments which have been used to solve a number of longstanding problems. The new strategically important developments are related to the names of V. Voevodsky (Fields Medal 2002), M. Rost, A. Suslin, I. Panin, M. Levine, F. Morel.

The principal aim of this project is to investigate enriched motivic homotopy theory. It is hoped that its study will shed light on some classical problems in A^1-topology. We propose to use its methods to construct various triangulated categories of motives, one of the central objects of study in modern A^1-topology. We believe that these constructions will have important computational advantages. The homotopy-theoretic outlook that we develop is likely to be useful in other areas of mathematics such as algebraic topology and non-commutative geometry.

The research will be undertaken in the Department of Mathematics, Swansea University.
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Organisation Website: http://www.swan.ac.uk