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Title: Operations in (Hermitian) k-theory and related topics
Author: Zanchetta, Ferdinando
ISNI:       0000 0004 9357 9081
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2019
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Since the very beginning of K-theory, operations like the lambda or the Adams operations played a crucial role into the statement and the solution of many important problems. They followed the evolution of K-theory at any stage, generalizing and refining themselves as long as the theory was growing. The main objective of this thesis is to study a generalisation of the results contained in the works of Joel Riou from the category of smooth schemes to the category of schemes having an ample family of line bundles. In particular we show that it is possible to give a special lambda ring structure to K-theory seen as an element of the Zariski homotopy category of simplicial presheaves over the site of divisorial schemes over some regular base and that this structure is uniquely determined by the one we have on the level of the ordinary K-theory of vector bundles. This is done using homotopical methods and proving along the way that divisorial schemes can be embedded into smooth ones: result which is of independent interest. We then compare our construction with other older constructions and we deduce as an application of our main theorems some interesting results, including an Adams-Riemann-Roch theorem. Finally, we show that the methods of this thesis and the ones of Riou can be applied in some cases also to Hermitian K-theory.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics