Lin, Qiang (2004) Bloch-Kato conjecture for the adjoint of H1(X0(N)) with integral Hecke algebra. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-11182003-084742
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 H^1(X_0(N)) for prime N and where T is the (commutative) integral Hecke algebra for cusp forms of weight 2 and the congruence group [Gamma_0](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_l 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|
|Thesis Availability:||Restricted to Caltech community only|
|Defense Date:||19 September 2003|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||06 Feb 2004|
|Last Modified:||26 Dec 2012 03:10|
- Final Version
Restricted to Caltech community only
See Usage Policy.
Repository Staff Only: item control page