Skip to primary content
Skip to secondary content

Stacks Project Blog

Algebraic stacks and open source algebraic geometry

Stacks Project Blog

Main menu

  • Home
  • About

Search Results for: challenge

Challenge Accepted

Posted on October 25, 2016 by Johan

Remember this challenge? Probably not. But wait, don’t click! Namely, I will do something more general in this post. Suppose we have a ring A and a contravariant functor F on (Sch/A) with the following properties: F satisfies the sheaf property … Continue reading →

Posted in Uncategorized

Another challenge

Posted on October 25, 2012 by Johan

Let A —> B be a finitely presented ring map. Let M be a finitely presented B-module flat over A. Then the projective dimension of M as an A-module is at most 1. This follows from a result of Jensen … Continue reading →

Posted in Uncategorized

Challenge

Posted on October 24, 2012 by Johan

Let f : X —> B be a morphism of algebraic spaces. Let u : F —> G be a map of quasi-coherent O_X-modules. Consider the functor F : (Sch/B) —> (Sets), T |—> singleton if u_T is zero and … Continue reading →

Posted in Uncategorized

A challenge

Posted on February 16, 2011 by Johan

Here is a challenge to an commutative algebraist out there. Give a direct algebraic proof of the following statement (see Lemma Tag 05U9): Let A —> B be a local ring homomorphism which is essentially of finite type. Let N … Continue reading →

Posted in Uncategorized

Minimal Cech coverings

Posted on March 22, 2020 by Johan

Please don’t read this unless you want to be distracted in these difficult times and you enjoy thinking about elementary problems in etale cohomology. I am going to pose a challenge computing etale cohomology by Cech coverings. The setting. We … Continue reading →

Posted in Uncategorized

Comments and the Stacks project

Posted on July 20, 2012 by Johan

As discussed here the new Stacks project website allows you to leave comments. In this blog post I’d like to advertise this as a fun activity and as well discuss what kind of comments I’d like to encourage. Before we … Continue reading →

Posted in Uncategorized

Purity

Posted on February 16, 2011 by Johan

Let f : X —> S be a morphism of finite type. The relative assassin Ass(X/S) of X/S is the set of points x of X which are embedded points of their fibres. So if f has reduced fibres or … Continue reading →

Posted in Uncategorized

Splitting chapters

Posted on March 28, 2010 by Johan

So I was wondering if it would maybe help to split the chapters in the stacks project into shorter chapters. To do this I wrote a python script that can automatically fix tags and references that point to the wrong … Continue reading →

Posted in Uncategorized

Blogroll

  • aisejohan
  • Johan de Jong
  • Stacks project
  • Stacks project on github
  • Stacks tools on github
  • Stacks website on github

RSS Recent Posts

  • Infinite dimensional de Rham cohomology
  • Updated Stacks Project
  • Postdoc position
  • Endomorphisms of the Koszul complex
  • Workshop

RSS Recent Comments

  • Comment on A Jouanolou device by Mateo Carmona
  • Comment on Sections vs retractions by Johan
  • Comment on Sections vs retractions by Jason Starr
  • Comment on Supports of flat modules by Supports of flat modules, part B | Stacks Project Blog
  • Comment on Supports of flat modules by Johan

RSS Development Log

  • Make sure the complexes are as desired
  • Which U?
  • Typo in algebra
  • Fix a proof in more-algebra
  • Typo in proetale
  • Typo
  • Explain z
  • Missing a
  • Typos in limits
  • Give a name to

RSS Stacks project comments

  • #10502 on tag 00ME by Stacks Project
  • #10501 on tag 091G by Stacks Project
  • #10500 on tag 06Y0 by Stacks Project
  • #10499 on tag 015L by Stacks Project
  • #10498 on tag 09GB by Stacks Project

Archives

  • April 2025 (1)
  • June 2024 (1)
  • October 2023 (1)
  • September 2023 (1)
  • August 2023 (1)
  • June 2023 (1)
  • March 2023 (1)
  • January 2023 (1)
  • August 2022 (1)
  • May 2022 (1)
  • February 2022 (2)
  • December 2021 (1)
  • July 2021 (1)
  • May 2021 (2)
  • April 2021 (4)
  • December 2020 (1)
  • November 2020 (1)
  • June 2020 (1)
  • May 2020 (1)
  • April 2020 (1)
  • March 2020 (6)
  • January 2020 (1)
  • September 2019 (2)
  • June 2019 (1)
  • May 2019 (3)
  • April 2019 (2)
  • February 2019 (3)
  • January 2019 (2)
  • November 2018 (1)
  • October 2018 (3)
  • May 2018 (3)
  • February 2018 (3)
  • August 2017 (1)
  • July 2017 (2)
  • February 2017 (1)
  • January 2017 (1)
  • October 2016 (1)
  • September 2016 (1)
  • June 2016 (2)
  • April 2016 (2)
  • March 2016 (1)
  • February 2016 (3)
  • December 2015 (2)
  • October 2015 (1)
  • September 2015 (2)
  • August 2015 (2)
  • July 2015 (1)
  • June 2015 (2)
  • April 2015 (2)
  • March 2015 (1)
  • February 2015 (2)
  • January 2015 (2)
  • December 2014 (1)
  • November 2014 (1)
  • October 2014 (3)
  • September 2014 (3)
  • August 2014 (4)
  • July 2014 (19)
  • June 2014 (8)
  • May 2014 (1)
  • April 2014 (1)
  • March 2014 (1)
  • February 2014 (2)
  • January 2014 (2)
  • December 2013 (1)
  • November 2013 (1)
  • September 2013 (4)
  • August 2013 (11)
  • July 2013 (26)
  • June 2013 (5)
  • May 2013 (1)
  • April 2013 (1)
  • March 2013 (1)
  • February 2013 (9)
  • January 2013 (6)
  • December 2012 (1)
  • October 2012 (6)
  • September 2012 (3)
  • August 2012 (2)
  • July 2012 (11)
  • June 2012 (3)
  • May 2012 (10)
  • April 2012 (3)
  • March 2012 (6)
  • February 2012 (3)
  • January 2012 (1)
  • December 2011 (3)
  • November 2011 (2)
  • October 2011 (9)
  • September 2011 (5)
  • August 2011 (4)
  • July 2011 (4)
  • June 2011 (6)
  • May 2011 (6)
  • April 2011 (14)
  • March 2011 (6)
  • February 2011 (10)
  • January 2011 (8)
  • December 2010 (8)
  • November 2010 (3)
  • October 2010 (6)
  • September 2010 (9)
  • August 2010 (7)
  • July 2010 (13)
  • June 2010 (11)
  • May 2010 (11)
  • April 2010 (10)
  • March 2010 (8)
  • February 2010 (9)
  • January 2010 (9)
Proudly powered by WordPress