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Bloch-Kato Conjecture for the Adjoint of H¹(X₀(N)) with Integral Hecke Algebra


Lin, Qiang (2004) Bloch-Kato Conjecture for the Adjoint of H¹(X₀(N)) with Integral Hecke Algebra. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QD4X-J291.


Let M be a motive that is defined over a number field and admits an action of a finite dimensional semisimple Q-algebra T. David Burns and Matthias Flach formulated a conjecture, which depends on a choice of Z-order T in T, for the leading coefficient of the Taylor expansion at 0 of the T-equivariant L-function of M. For primes l outside a finite set we prove the l-primary 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 Bloch-Kato conjecture and the other a slight variant of what is defined by A. Wiles. A result on the Fontaine-Laffaille modules with coefficients in a local ring finite free over Z is obtained.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:adjoint motives; Bloch-Kato conjecture; Burns-Flach 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):
  • Flach, Matthias
Thesis Committee:
  • Flach, Matthias (chair)
  • Ramakrishnan, Dinakar
  • Goins, Edray
  • Aschbacher, Michael
Defense Date:19 September 2003
Record Number:CaltechETD:etd-11182003-084742
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4595
Deposited By: Imported from ETD-db
Deposited On:06 Feb 2004
Last Modified:20 Jan 2021 23:38

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