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Abelian l-Adic Representations and Elliptic Curves : Research Notes in Mathematics (A K Peters), Vol 7 - Jean-Pierre Serre

Abelian l-Adic Representations and Elliptic Curves

Research Notes in Mathematics (A K Peters), Vol 7

Hardcover Published: 1st April 1998
ISBN: 9781568810775
Number Of Pages: 208

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This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one finds a nice correspondence between the l-adic representations and the linear representations of some algebraic groups (now called Taniyama groups). The last chapter handles the case of elliptic curves with no complex multiplication, the main result of which is that the image of the Galois group (in the corresponding l-adic representation) is "large."

l-adic Representations
The notion of an l-adic representation
l-adic representations of number fields
Equipartition and L-functions
The Groups S[subscript m]
Construction of T[subscript m] and S[subscript m]
Structure of T[subscript m] and applications
Killing arithmetic groups in tori
Locally Algebraic Abelian Representations
The local case
The global case
The case of a composite of quadratic fields
Hodge-Tate decompositions and locally algebraic representations
l-adic Representations Attached to Elliptic Curves
The Galois modules attached to E
Variation of G[subscript l] and G[subscript l] with l
Local results
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781568810775
ISBN-10: 1568810776
Series: Research Notes in Mathematics (A K Peters), Vol 7
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 208
Published: 1st April 1998
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 16.51  x 1.91
Weight (kg): 0.45
Edition Number: 3

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