Outline

Topological groups are ubiquitous in mathematics: they appear as real or complex vector spaces in functional analysis, as profinite groups in Galois theory and étale cohomology, and as adic rings and modules in formal and nonarchimedean geometry. But topological abelian groups do not form an abelian category: the inclusion R^disc → R of the reals with discrete topology into the reals with their usual topology is both injective and surjective, but not an isomorphism.

Condensed abelian groups, after Clausen and Scholze (and parallel work by Barwick and Haine), aim to fix these problems. They form an abelian category with very good formal properties, containing locally compact abelian groups as a full subcategory.

The first two meetings of this intercity seminar are dedicated to understanding the foundations of condensed abelian groups and their relation to locally compact abelian groups. We then proceed to the formalism of solid abelian groups, which are the analogue of adically complete abelian groups. In the final session, we use these to give a generalisation of Serre–Grothendieck duality to the case of non-proper morphisms of schemes.

Organisers

The local organisers are as follows (in chronological order, as well as reverse alphabetical by surname):

Universiteit van Amsterdam	Lenny Taelman
Radboud Universiteit Nijmegen	Ben Moonen
Universiteit Leiden	David Holmes
Universiteit Utrecht	Remy van Dobben de Bruyn

If you would like to give a talk, or if you have questions about the contents of your talk, it's probably easiest to write to Lenny and/or Ben. For practical matters about the meetings, please write to the local organiser. For any other questions, you can write to Remy.

References

The main reference is:

Other references you may consult:

Schedule

Click on the red names to see a brief abstract of each talk (where available). The schedule below may be updated with further details, but should otherwise be somewhat stable.

7 October: Universiteit van Amsterdam

Lecture room L1.01 in LAB42. This is a new building on Science Park, see https://goo.gl/maps/GLRa7hr7i3fWahkT7.

21 October: Radboud Universiteit Nijmegen

Linnaeus building, room LIN2. This is the building to the right (south) of the Huygens building.

Notes for Ben's talk and Remy's talk.

11 November: Universiteit Leiden

Snellius building, room 174 (first floor, above the main entrance).

Notes for Simon's talk.

2 December: Universiteit Utrecht

Buys Ballot building, room 165. Enter through the Victor J. Koningsberger building, go up the big stairs to the first floor, and keep walking straight towards the end of the first floor of Buys Ballot.