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On the equivariant Tamagawa number conjecture

Citation

Navilarekallu, Tejaswi (2006) On the equivariant Tamagawa number conjecture. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05242006-225912

Abstract

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
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Flach, Matthias
Thesis Committee:
  • Flach, Matthias (chair)
  • Ramakrishnan, Dinakar
  • Wambach, Eric
  • Dimitrov, Mladen
Defense Date:8 May 2006
Record Number:CaltechETD:etd-05242006-225912
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05242006-225912
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2017
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:31 May 2006
Last Modified:26 Dec 2012 02:45

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