The Rising Sea http://therisingsea.org la mer qui monte Sun, 17 Jan 2010 17:11:34 +0000 http://backend.userland.com/rss092 en Update Unfortunately this website was compromised in the recent wave of attacks on Wordpress blogs, but hopefully everything is now OK. I’d like to thank Graham Leuschke for sounding the alarm.

In other news, I’ve been thinking lately about duality in Orlov’s singularity category (or, for the commutative algebraists, the stable category of Cohen-Macaulay modules) and [...]

]]> http://therisingsea.org/?p=27 Talk slides I have the good fortune of being in Barcelona, at the Centre de Recerca Matematica, for the month of November. Yesterday I spoke on my thesis research “The mock homotopy category of projectives and Grothendieck duality” as part of a workshop on derived categories being organised by Leovigildo Alonso Tarrío, Ana Jeremías López and Amnon [...]

]]> http://therisingsea.org/?p=18 Triangulated Category Notes I’ve improved some statements in Triangulated Categories (TRC). For the curious: the changes are in the section on Localisation Sequences, where some inelegant writing exposed my lack of understanding at the time.

]]> http://therisingsea.org/?p=16 Notes Update Lately I’ve been occupied with research, so there still isn’t much new in the notes. In this update the referencing (which was shocking before) has been improved a little and there are some extra historical remarks in DCOQS and DTC. If you’re reading through any of the following notes you may benefit from several minor [...]

]]> http://therisingsea.org/?p=15 Notes Update This month there are only some minor additions and corrections to existing notes:

Derived Categories (DTC) In Section 5.1 on “Split Direct Limits” I made use of a complicated result with a long proof. This has now been omitted in favour of a weaker result with a much easier proof, that is nonetheless sufficient for [...]

]]> http://therisingsea.org/?p=14 Notes Update There have been various small changes to my notes, so if you’re using several of them you should update to the newest versions to avoid incorrect references. The only major addition this time is in DCOQS:

Derived Categories of Quasi-coherent Sheaves (DCOQS) Added a section on “invertible complexes” which are complexes in the derived category [...]

]]> http://therisingsea.org/?p=13 Study Software A few people have already downloaded my simple application Study for managing mathematics notes. An unadvertised feature of the current version is the ability to create cross-references between results in different files. If you download any of my mathematics notes you will probably notice “coloured” links of the form (MRS, Proposition 6). Keeping such references [...]

]]> http://therisingsea.org/?p=12 Notes Update Nothing of great excitement in this month’s notes update. I’ve made some minor additions and changes to existing notes:

Derived Categories of Quasi-coherent Sheaves (DCOQS) The section on the projection formula has been updated with a few results from SGA that I’ve updated to modern standards (i.e. some boundedness hypotheses were removed). This includes the [...]

]]> http://therisingsea.org/?p=11 Notes Update Another month, another update. Today I’ve added one new note on ample families of sheaves and updated two other notes with substantial new content:

New Notes: Ample Families (AMF) If you grew up on Hartshorne’s book like I did, then you may have only encountered ample sheaves on a noetherian scheme. In fact the original definition [...]

]]> http://therisingsea.org/?p=10 Notes Update Today I’ve posted one new set of notes and made various changes to other notes. The major changes:

New notes: Derived Categories of Quasi-coherent Sheaves (DCOQS) In algebraic geometry it is the derived categories of quasi-coherent (or coherent) sheaves that are usually of interest. For the unbounded derived category a lot of nice results are [...]

]]> http://therisingsea.org/?p=9