Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01qf85nf67q
Full metadata record
DC FieldValueLanguage
dc.contributor.advisorSkinner, Christopher
dc.contributor.authorSangiovanni Vincentelli, Marco Antonio
dc.contributor.otherMathematics Department
dc.date.accessioned2024-07-24T16:32:02Z-
dc.date.available2024-07-24T16:32:02Z-
dc.date.created2024-01-01
dc.date.issued2024
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01qf85nf67q-
dc.description.abstractThis dissertation studies Euler Systems and their arithmetic applications. Euler Systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of $L$-functions. However, despite their importance in foundational conjectures in number theory like the Bloch--Kato conjecture, only a handful of provably non-trivial Euler systems have been constructed to date. A significant obstacle in constructing Euler Systems lies in producing candidate Galois cohomology classes. This thesis presents a method to overcome this obstacle without relying on rare motivic classes. In joint work with C. Skinner, I use Eisenstein classes on Siegel threefolds to construct a cyclotomic Euler System for the adjoint of an elliptic modular form. I also construct integral absolute \'etale classes on modular curves associated to theta series at inert primes. These theta classes should give new insight into the Iwasawa main conjecture for modular forms over quadratic imaginary fields at inert primes.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherPrinceton, NJ : Princeton University
dc.subjectAdjoint
dc.subjectBloch--Kato
dc.subjectEuler System
dc.subjectIwasawa Theory
dc.subjectModular forms
dc.subjectSelmer Group
dc.subject.classificationMathematics
dc.titleCrafting Euler Systems: Beyond the Motivic Mold
dc.typeAcademic dissertations (Ph.D.)
pu.date.classyear2024
pu.departmentMathematics
Appears in Collections:Mathematics

Files in This Item:
File Description SizeFormat 
SangiovanniVincentelli_princeton_0181D_15074.pdf1.87 MBAdobe PDFView/Download


Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.