Fdtxjr

What should be the ideal length of sentences in a blog post for ease of reading?

What does "tick" mean in this sentence?

Limit max CPU usage SQL SERVER with WSRM

Proving an identity involving cross products and coplanar vectors

Animation: customize bounce interpolation

Check if object is null and return null

Air travel with refrigerated insulin

Why didn’t Eve recognize the little cockroach as a living organism?

Do I have to know the General Relativity theory to understand the concept of inertial frame?

Ways of geometrical multiplication

How do I Interface a PS/2 Keyboard without Modern Techniques?

Difference between shutdown options

The Digit Triangles

Showing mass murder in a kid's book

Is there a RAID 0 Equivalent for RAM?

What is the meaning of "You've never met a graph you didn't like?"

Mimic lecturing on blackboard, facing audience

Anime with legendary swords made from talismans and a man who could change them with a shattered body

How to leave product feedback on macOS?

How to preserve electronics (computers, iPads and phones) for hundreds of years

Did I make a mistake by ccing email to boss to others?

In One Punch Man, is King actually weak?

Why is the principal energy of an electron lower for excited electrons in a higher energy state?

PTIJ: Which Dr. Seuss books should one obtain?

Is there a fiber bundle/espace-etale interpretation of sheaves on a Grothendieck site

Local vs. global in the definition of a sheafPullback of sheaves and pullback of schemesDifferentiating (pre)sheaves by their stalks and etale topologiesMoving from sheaves over spaces to sheaves over sitesFunctor of points definition of a space modeled on a siteWhat does the pushforward of an etale sheaf over a field correspond to in terms of Galois cohomology?Why the Skyscraper Sheaf is Named as Such, Intuition and InterpretationSheaves on a scheme compared with sheaves on its étale siteCharacterizing Morphism of SheavesDifferent notions of torsors in algebraic geometry

2

0

$begingroup$

Whenever I'm doing sheaf things and I have a construction that involves sheafifying, I find it convenient to think "the thing that has the same stalks but sections must be locally trivial sections to espace etale" - it's a nice way to think of/characterize sheafification, sections of sheaves, define pullbacks, etc.

Can we do the same thing on a general, reasonable site (e.g. etale, flat, etc), i.e. for say $mathscrF$ a sheaf on a scheme $X$ on the etale site, can we form something like $coprod mathscrF_x$ as $x$ runs over geometric points, suitably "Grothendieck topologized" so that the Grothendieck continuous sections over $U to X$ are precisely $mathscrF(U to X)$?

algebraic-geometry category-theory sheaf-theory etale-cohomology grothendieck-topologies

share|cite|improve this question

edited Mar 14 at 18:00

edgarlorp

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is a "Grothendieck continuous" morphism? And what category is it supposed to be a morphism of?
  $endgroup$
  – Kevin Carlson
  Mar 14 at 16:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't know, that's part of the question of what such a formulation would mean.
  $endgroup$
  – edgarlorp
  Mar 14 at 17:53
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ok. The problem is that Grothendieck topologies very specifically generalize the property of topological spaces that they produce a sheaf theory, and not that they produce a notion of continuous map.
  $endgroup$
  – Kevin Carlson
  Mar 14 at 19:51
  

  
  
  
  

add a comment | 

2

0

$begingroup$

Whenever I'm doing sheaf things and I have a construction that involves sheafifying, I find it convenient to think "the thing that has the same stalks but sections must be locally trivial sections to espace etale" - it's a nice way to think of/characterize sheafification, sections of sheaves, define pullbacks, etc.

Can we do the same thing on a general, reasonable site (e.g. etale, flat, etc), i.e. for say $mathscrF$ a sheaf on a scheme $X$ on the etale site, can we form something like $coprod mathscrF_x$ as $x$ runs over geometric points, suitably "Grothendieck topologized" so that the Grothendieck continuous sections over $U to X$ are precisely $mathscrF(U to X)$?

algebraic-geometry category-theory sheaf-theory etale-cohomology grothendieck-topologies

share|cite|improve this question

edited Mar 14 at 18:00

edgarlorp

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is a "Grothendieck continuous" morphism? And what category is it supposed to be a morphism of?
  $endgroup$
  – Kevin Carlson
  Mar 14 at 16:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't know, that's part of the question of what such a formulation would mean.
  $endgroup$
  – edgarlorp
  Mar 14 at 17:53
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ok. The problem is that Grothendieck topologies very specifically generalize the property of topological spaces that they produce a sheaf theory, and not that they produce a notion of continuous map.
  $endgroup$
  – Kevin Carlson
  Mar 14 at 19:51
  

  
  
  
  

add a comment | 

$begingroup$

Whenever I'm doing sheaf things and I have a construction that involves sheafifying, I find it convenient to think "the thing that has the same stalks but sections must be locally trivial sections to espace etale" - it's a nice way to think of/characterize sheafification, sections of sheaves, define pullbacks, etc.

Can we do the same thing on a general, reasonable site (e.g. etale, flat, etc), i.e. for say $mathscrF$ a sheaf on a scheme $X$ on the etale site, can we form something like $coprod mathscrF_x$ as $x$ runs over geometric points, suitably "Grothendieck topologized" so that the Grothendieck continuous sections over $U to X$ are precisely $mathscrF(U to X)$?

algebraic-geometry category-theory sheaf-theory etale-cohomology grothendieck-topologies

share|cite|improve this question

edited Mar 14 at 18:00

edgarlorp

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

$endgroup$

share|cite|improve this question

edited Mar 14 at 18:00

edgarlorp

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

share|cite|improve this question

edited Mar 14 at 18:00

edgarlorp

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076

asked Mar 14 at 7:26

edgarlorpedgarlorp

1076