Navilarekallu, Tejaswi (2006) On the equivariant Tamagawa number conjecture. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05242006-225912
For a finite Galois extension $K/Q$ of number fields with Galois group $G$ and a motive $M = M' otimes h^0(Spec(K))(0)$ with coefficients in $Q[G]$, the equivariant Tamagawa number conjecture relates the special value $L^*(M,0)$ of the motivic $L$-function to an element of $K_0(Z[G];R)$ constucted via complexes associated to $M$. The conjecture for nonabelian groups $G$ is very much unexplored. In this thesis, we will develop some techniques to verify the conjecture for Artin motives and motives attached to elliptic curves. In particular, we consider motives $h^0(Spec(K))(0)$ for an $A_4$-extension $K/Q$ and, $h^1 (E imes Spec(L))(1)$ for an $S_3$-extension $L/Q$ and an elliptic curve $E/Q$.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Subject Keywords:||Equivariant Tamagawa number Conjecture; modular symbols; period isomorphism; Tate sequences|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||8 May 2006|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||31 May 2006|
|Last Modified:||26 Dec 2012 02:45|
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