The Second Case of Fermat’s Last Theorem

1982 ◽  
pp. 167-183
Author(s):  
Lawrence C. Washington
Keyword(s):  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

Fermat's Last Theorem

1986 ◽  
Vol 59 (2) ◽  
pp. 76 ◽  
Author(s):  
Jonathan P. Dowling
Keyword(s):  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

Alcune riflessioni su Fermat’s Last Theorem

2005 ◽  
pp. 267-272
Author(s):  
Mirella Manaresi ◽  
Angelo Vistoli
Keyword(s):  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem

scholarly journals Proof of de Smit’s conjecture: a freeness criterion

2017 ◽  
Vol 153 (11) ◽  
pp. 2310-2317
Author(s):  
Sylvain Brochard
Keyword(s):  
Complete Intersection ◽  
Local Rings ◽  
Embedding Dimension ◽  
Fermat's Last Theorem ◽  
Multiplicity One ◽  
Fermat’S Last Theorem ◽  
Invent Math

Let $A\rightarrow B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond’s criterion [The Taylor–Wiles construction and multiplicity one, Invent. Math. 128 (1997), 379–391, Theorem 2.1]. We also prove that if there is a nonzero $A$-flat $B$-module, then $A\rightarrow B$ is flat and is a relative complete intersection. Then we explain how this result allows one to simplify Wiles’s proof of Fermat’s last theorem: we do not need the so-called ‘Taylor–Wiles systems’ any more.

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