Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.721690
Title: Non-commutative Iwasawa theory with (φ,Γ)-local conditions over distribution algebras
Author: Zähringer, Yasin Hisam Julian
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2017
Availability of Full Text:
Access from EThOS:
Access from Institution:
Abstract:
In this thesis we formulate a natural non-commutative Iwasawa Main Conjecture for motives which fulfil the Dabrowski-Panchishkin condition on the level of (φ,Γ)-modules. The basic framework we employ is still Fukaya-Kato’s but we work systematically over Schneider-Teitelbaum’s distribution algebras of compact p-adic Lie groups instead of Iwasawa algebras. This allows us to consider as local conditions not just subrepresentations of the p-adic realisation which fulfil the Dabrowski-Panchishkin conditions but also sub-(φ,Γ)-modules which fulfil the analogous Dabrowski-Panchishkin conditions. We then combine this with Pottharst’s Selmer complexes and a generalisation of Nakamura’s Local Epsilon Conjecture for (φ,Γ)-modules to conjecturally define p-adic L-functions. We prove that the validity of our main conjecture for these p-adic L-functions follows from the validity of Fukaya-Kato’s Equivariant Tamagawa Number Conjecture and our generalisation of Nakamura’s Local Epsilon Conjecture. Moreover we are also able to compute the values of these p-adic L-functions at motivic points. Our formalism allows us, for example, to unify the GL2-main conjecture of elliptic curves which have either ordinary or supersingular reduction at p. In addition, we can use our formalism to give a new, and very natural, interpretation of Pollack’s ±-construction in the context of supersingular elliptic curves and we are hopeful that this new interpretation will in the future lead to the construction of natural non-commutative generalizations.
Supervisor: Kakde, Mahesh Ramesh ; Burns, David John Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.721690  DOI: Not available
Share: