CaltechTHESIS
  A Caltech Library Service

On the Equivariant Tamagawa Number Conjecture

Citation

Navilarekallu, Tejaswi (2006) On the Equivariant Tamagawa Number Conjecture. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7HZ0-F068. https://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' ⊗ h⁰(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 K₀(Z[G];R) constructed 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 h⁰(Spec(K))(0) for an A₄-extension K/Q and, h¹ (E x Spec(L))(1) for an S₃-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:https://resolver.caltech.edu/CaltechETD:etd-05242006-225912
DOI:10.7907/7HZ0-F068
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:08 Apr 2020 18:43

Thesis Files

[img]
Preview
PDF - Final Version
See Usage Policy.

525kB

Repository Staff Only: item control page