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From: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=90=E6=AD=A3=E8=88=AA?= <jonathan.chiche@polytechnique.edu>
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Subject: Re: Smooth and proper functors
Date: Thu, 16 Apr 2009 15:46:53 +0200
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To: Hasse Riemann <rafaelb77@hotmail.com>, <categories@mta.ca>
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Hi,

The following paper is very clear, I'm currently learning the basics =20
of the subject with it: http://people.math.jussieu.fr/~maltsin/ps/=20
asphbl.ps. It's written in French. Another member of this mailing-=20
list has asked me to translate it in English, I may be able to send =20
you a rough translation in a few weeks.

Best,

Jonathan

Le 15 avr. 09 =E0 15:45, Hasse Riemann a =E9crit :

> Hi category gurus and categorists
>
>
>
> I have many questions about category theory but i start with one.
>
>
>
> 1>
>
> What are smooth functors and proper functors, originating in =20
> pursuing stacks?
>
> Both nontechnically and technicaly.
>
>
>
> I know they are dual to each other and that they are characterized =20
> by cohomological properties
>
> inspired by the proper or smooth base change theorem in algebraic =20
> geometry, but what is the relation?
>
> (I don't know the statement of the theorems)
>
>
>
> Finally, what are smooth and proper functors good for?
>
> Are smooth and proper functors fibrations and cofibrations or =20
> Grothendieck fibrations and
>
> Grothendieck op-fibrations in some model categories or derivators?
>
>
>
> The only thing i could find about smooth and proper functors on =20
> internet is the last entrance in
> http://golem.ph.utexas.edu/category/2008/01/=20
> geometric_representation_theor_18.html
>
>
>
> Best regards
>
> Rafael Borowiecki