Re: Simplified definition of scheme proposed by Grothendieck

Re: Simplified definition of scheme proposed by Grothendieck

[David Roberts]

Ah, thanks, that's exactly the sort of explanation I was hoping for.
And after I sent my message, I thought that Gaeta's notes might be
relevant (they cam be found at
http://www.math.jussieu.fr/~leila/grothendieckcircle/FuncAlg.pdf)

Thanks also to those that responded privately. Thomas Holder in
particular pointed to further messages from Lawvere reproduced at

http://mathoverflow.net/a/52894/4177

in the context of the general concept of Nullstellensatz.

Best regards,

David

On 29 November 2014 at 00:23, Venkata Rayudu Posina
<posinavrayudu@gmail.com> wrote:
> The following post
>
> http://permalink.gmane.org/gmane.science.mathematics.categories/2228
>
> might answer the following question:
>
> On Thu, Nov 27, 2014 at 10:34 PM, David Roberts
> <david.roberts@adelaide.edu.au> wrote:
>> Dear all,
>>
>> in the TAC reprint 'Comments on the development of topos theory', Lawvere writes
>>
>>> during that [1973 stay in Buffalo, Grothendieck] also advocated the
>>> abandonment of his earlier complicated definition of 'scheme', but
>>> unfortunately the simpler alternative he offered does not seem to have
>>> found its way into the textbooks
>>
>> What would this simplified definition be?



-- 
Dr David Roberts
Research Associate
School of Mathematical Sciences
University of Adelaide
SA 5005
AUSTRALIA


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Re: Simplified definition of scheme proposed by Grothendieck

[Venkata Rayudu Posina]

The following post

http://permalink.gmane.org/gmane.science.mathematics.categories/2228

might answer the following question:

On Thu, Nov 27, 2014 at 10:34 PM, David Roberts
<david.roberts@adelaide.edu.au> wrote:
> Dear all,
>
> in the TAC reprint 'Comments on the development of topos theory', Lawvere writes
>
>> during that [1973 stay in Buffalo, Grothendieck] also advocated the
>> abandonment of his earlier complicated definition of 'scheme', but
>> unfortunately the simpler alternative he offered does not seem to have
>> found its way into the textbooks
>
> What would this simplified definition be?


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Simplified definition of scheme proposed by Grothendieck

[David Roberts]

Dear all,

in the TAC reprint 'Comments on the development of topos theory', Lawvere writes

> during that [1973 stay in Buffalo, Grothendieck] also advocated the 
> abandonment of his earlier complicated definition of 'scheme', but 
> unfortunately the simpler alternative he offered does not seem to have 
> found its way into the textbooks

What would this simplified definition be?

Also, reference is made to a document held in Jack Duskin's files made
during this visit. If this document still exists, I would exhort
whoever has it to donate it, or a high-quality scan of it, to the
Grothendieck Circle people. After G's passing, his works have gone
back online, apparently with the permission of his family, see

http://www.grothendieckcircle.org/

Best regards,

David

-- 
Dr David Roberts
Research Associate
School of Mathematical Sciences
University of Adelaide
SA 5005
AUSTRALIA


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]