Witt vectors and their applications in arithmetic algebraic geometry

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This project aims to continue the development of arithmetic algebraic geometry. This is the field of fundamental mathematics that forms the basis for much of cryptography and coding theory, which are the fields of applied mathematics that allow for secure and efficient electronic communication. The approach will be to apply recent advances in the theory of global Witt vectors to resolve some open questions involving numerical properties of polynomial equations. This is expected to lead to advances in a field which is of fundamental importance in mathematics generally and which is also the basis of secure internet communication.