Student seminar

## Goal

This semester the seminar will be organized more along the lines of a reading group: first we discuss a part of the text that we read at home, then someone gives a lecture about what follows. We will repeat this a few times whilst working through Chan's Lectures on orders.

Once this is done we will take a look the special case of (maximal orders) on curves and surfaces. We will discuss Artin's conjecture (which is the analogue of the Enriques--Kodaira classification for smooth projective surfaces) and the notion of weighted noncommutative curves. An important reference will be Artin--de Jong's Stable orders over surfaces.

## Schedule

- February 10
- Reduced trace and basic properties of maximal orders
- by Dennis Presotto, in G.005, at 11h00
- February 17
- Structure theory of complete division algebras
- by Jens Hemelaer, in G.005, at 11h00
- February 24
- Ramification theory
- by Pieter Belmans, in G.005, at 11h00
- March 9
- The Artin--Mumford sequence
- by Jens Hemelaer, in G.005, at 11h00
- March 23
- Weighted noncommutative projective curves
- by Pieter Belmans, in G.005, at 11h00
- April 13
- Hilbert schemes of points and Brauer--Severi schemes for orders
- by Pieter Belmans, in G.005, at 11h00
- Introducing Cayley–Hamilton algebras (notes)
- by Jens Hemelaer, in G.005, at 12h00
- April 20
- Cayley–Hamilton algebras and orders
- by Jens Hemelaer, in G.005, at 11h00
- The Brauer–Severi scheme for an order on a curve
- by Pieter Belmans, in G.005, at 12h00
- April 27
- The Brauer–Severi scheme for an order on a curve
- by Pieter Belmans, in G.016, at 11h00
- Representation variety versus Brauer–Severi schemes
- by Jens Hemelaer, in G.016, at 12h00
- May 11
- The étale-local structure of $\mathrm{trep}_nA$ for $A\in\mathrm{alg}@n$
- by Jens Hemelaer, in G.016, at 11h00

## References

In due time I might add these.

home