Grothendieck introduces, on the top of p. 209 of the Tohoku paper, the notation U_{i_0..i_p} without explanation and uses it again over the next couple pages. Here {U_i} is an open cover of a space X and I have reason to believe that this stands for the intersection of U_{i_j}. Can anyone confirm this? Or give an alternate explanation? The context is that of a claim that (when A is a sheaf) and "every U_{i_0..i_p} is A-acyclic, then"... and that awfully like the definition of a simple cover. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On Mon, Aug 30, 2010 at 10:18:30AM -0400, Michael Barr wrote:
Grothendieck introduces, on the top of p. 209 of the Tohoku paper, the notation U_{i_0..i_p} without explanation and uses it again over the next couple pages. Here {U_i} is an open cover of a space X and I have reason to believe that this stands for the intersection of U_{i_j}. Can anyone confirm this? Or give an alternate explanation?
The context is that of a claim that (when A is a sheaf) and "every U_{i_0..i_p} is A-acyclic, then"... and that awfully like the definition of a simple cover.
I have absolutely no idea as to what Grothendieck meant, but the notation you describe is quite common in (algebraic) topology and means what you "have reason to believe" that it means. Andrew [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I am wondering, nobody can read the mathematics and come up with what Grothendieck meant !!! after all, this is not philosophy or psicology !! Andrew Stacey wrote:
On Mon, Aug 30, 2010 at 10:18:30AM -0400, Michael Barr wrote:
Grothendieck introduces, on the top of p. 209 of the Tohoku paper, the notation U_{i_0..i_p} without explanation and uses it again over the next couple pages. Here {U_i} is an open cover of a space X and I have reason to believe that this stands for the intersection of U_{i_j}. Can anyone confirm this? Or give an alternate explanation?
The context is that of a claim that (when A is a sheaf) and "every U_{i_0..i_p} is A-acyclic, then"... and that awfully like the definition of a simple cover.
I have absolutely no idea as to what Grothendieck meant, but the notation you describe is quite common in (algebraic) topology and means what you "have reason to believe" that it means.
Andrew
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On 9/1/2010 12:21 PM, Eduardo J. Dubuc wrote:
I am wondering, nobody can read the mathematics and come up with what Grothendieck meant !!!
Eduardo raises an excellent point here. Which is more important for a contribution, its meaning or its influence? If the latter, a secondary question is, how was that influence achieved? Improved access to the contribution, e.g. via translation, may help those who understand the mathematics but not the French explain the influence, even if the original meaning remains obscure. Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I confess that I am a little bit confused about what Vaughan is saying. This promps me to repeat my posting in other words: If a mathematical statement is understood by a reader (the hypotesis, the conclusion and the proof) then the mathematical meaning of any particular notation used should come up by itself to this reader (that is, it should be clear for him that only one possible meaning for this particular notation would make the things work). Eduardo Vaughan Pratt wrote:
On 9/1/2010 12:21 PM, Eduardo J. Dubuc wrote:
I am wondering, nobody can read the mathematics and come up with what Grothendieck meant !!!
Eduardo raises an excellent point here. Which is more important for a contribution, its meaning or its influence?
If the latter, a secondary question is, how was that influence achieved? Improved access to the contribution, e.g. via translation, may help those who understand the mathematics but not the French explain the influence, even if the original meaning remains obscure.
Vaughan
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Hi - Grothendieck introduces, on the top of p. 209 of the Tohoku paper, the
notation U_{i_0..i_p} without explanation and uses it again over the next couple pages. Here {U_i} is an open cover of a space X and I have reason to believe that this stands for the intersection of U_{i_j}. Can anyone confirm this?
That's certainly what everyone uses this notation for nowadays, so it sounds like a very good guess. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (5)
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Andrew Stacey -
Eduardo J. Dubuc -
John Baez -
Michael Barr -
Vaughan Pratt