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From: Colin McLarty <colin.mclarty@case.edu>
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Subject: Re: A well kept secret?
Date: Wed, 23 Dec 2009 09:15:06 -0500
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2009/12/22 Tom Leinster <tl@maths.gla.ac.uk>:

substantially understates

> [as to] "algebraic geometers" because it suggests that the
> anti-category theory backlash in that influential subject may be nearing
> an end.

the book about Wiles's proof of Fermat's Last Theorem

@BOOK{ModForms,
  editor =       "Cornell, Gary and Silverman, Joseph and Stevens, Glenn",
  TITLE =        "Modular Forms and {F}ermat's {L}ast {T}heorem",
  PUBLISHER =    "Springer-Verlag",
  YEAR =         "1997",
}

takes no explicit stand but is inevitably full of Grothendieck's
categorical tools.  More recently, from the beginning graduate level
to research we have books explicitly explaining or building on
Grothendieck's methods:


@BOOK{SzamuelyGal,
  AUTHOR =       "Szamuely, Tam{\'a)s",
  TITLE =        "Galois Groups and Fundamental Groups",
  PUBLISHER =    "Cambridge University Press",
  YEAR =         "2009",
}

@BOOK{FGAexplained,
  AUTHOR =       {Fantechi, Barbara and Angelo Vistoli, and Lothar
Gottsche, and Steven L. Kleiman,
      and Luc Illusie, and Nitin Nitsure},
  TITLE =        {Fundamental Algebraic Geometry: {G}rothendieck's
{FGA} Explained},
  PUBLISHER =    {American Mathematical Society},
  YEAR =         {2005},
}

@BOOK{LurieHigher,
  AUTHOR =       {Lurie, Jacob},
  TITLE =        {Higher Topos Theory},
  PUBLISHER =    {Princeton University Press},
  YEAR =         {2009},
}

and a series of printed or web-published works by Voevodsky.

There will be anti-Grothendieck backlashers always.  Life is like
that.  But for decades algebraic geometry at the top schools has been
impossible without Grothendieck tools and now that is being
mainstreamed.

best, Colin


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