# ANAGRAMS

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.