Citation
Lin, Qiang (2004) BlochKato Conjecture for the Adjoint of H¹(X₀(N)) with Integral Hecke Algebra. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QD4XJ291. https://resolver.caltech.edu/CaltechETD:etd11182003084742
Abstract
Let M be a motive that is defined over a number field and admits an action of a finite dimensional semisimple Qalgebra T. David Burns and Matthias Flach formulated a conjecture, which depends on a choice of Zorder T in T, for the leading coefficient of the Taylor expansion at 0 of the Tequivariant Lfunction of M. For primes l outside a finite set we prove the lprimary part of this conjecture for the specific case where M is the trace zero part of the adjoint of H¹(X₀(N)) for prime N and where T is the (commutative) integral Hecke algebra for cusp forms of weight 2 and the congruence group Γ₀(N), thus providing one of the first nontrivial supporting examples for the conjecture in a geometric situation where T is not the maximal order of T.
We also compare two Selmer groups, one of which appears in BlochKato conjecture and the other a slight variant of what is defined by A. Wiles. A result on the FontaineLaffaille modules with coefficients in a local ring finite free over Z_{ℓ} is obtained.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  adjoint motives; BlochKato conjecture; BurnsFlach conjecture; Modular forms 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Awards:  Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2003. 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  19 September 2003 
Record Number:  CaltechETD:etd11182003084742 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd11182003084742 
DOI:  10.7907/QD4XJ291 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4595 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  06 Feb 2004 
Last Modified:  20 Jan 2021 23:38 
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