The Proof of Fermat's Last Theorem
by: Nigel Boston
From the Introduction:
This book will describe the recent proof of Fermat’s Last Theorem by Andrew Wiles, aided by Richard Taylor, for graduate students and faculty with a reasonably broad background in algebra. It is hard to give precise prerequisites but a first course in graduate algebra, covering basic groups, rings and fields together with a passing acquaintance with number rings and varieties should suffice. Algebraic number theory (or arithmetical geometry, as the subject is more commonly called these days) has the habit of taking last year’s major result and making it background taken for granted in this year’s work. Peeling back the layers can lead to a maze of results stretching back over the
decades.
Contents:
Introduction.
Contents.
Chapter 1: History and overview.
Chapter 2: Profinite groups, complete local rings.
Chapter 3: Infinite Galois groups, internal structure.
Chapter 4: Galois representations from elliptic curves, modular
forms, group schemes.
Chapter 5: Invariants of Galois representations, semistable
representations.
Chapter 6: Deformations of Galois representations.
Chapter 7: Introduction to Galois cohomology.
Chapter 8: Criteria for ring isomorphisms.
Chapter 9: The universal modular lift.
Chapter 10: The minimal case.
Chapter 11: The general case.
Chapter 12: Putting it together, the final trick
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