**Ben Forrás’s**website

# Lecture notes

This is a list of courses I to some extent followed, or at least intended to follow, during my time at the University of Bonn, that is, from autumn 2017 to summer 2020, along with lecture notes and other related material, such as exercise sheets. **A more comprehensive list of courses can be found here.**

I have a habit of publishing some of my own handwritten notes here. This usually doesn’t happen on a regular schedule though. General warning: my notes contain several errors and typos, none of which are likely to get corrected in the foreseeable future. Caution is advised on the part of the reader.

Advice for printing scanned notes: the printer in the library prefers djvu files over pdfs. One should consider converting to djvu before sending files to the printer.

Some lecturers wipe their website clean every year, others move from university to university. This unfortunately results in broken links on this page. To remedy this despicable situation, one may capture some pages still online with the Wayback Machine. If you wish to join in on this practice, use this form, and don't forget to tick the box *Save outlinks*.

To lecturers: if you have a problem with something on this page, get in touch.

## Sommersemester 2020 (Nichtsemester)

**Selected Topics in Representation Theory: The Arithmetic of the Langlands program**, Johannes Anschütz**Selected Topics in Algebra: Topics in Automorphic Forms**, Edgar Assing**The moduli space of curves**, Johannes Schmitt- BASIS
- Course webpage with handwritten course notes uploaded after the Zoom lecture
**VaNTAGe seminar**- For the 2nd topic, see also Sutherland's lectures in the Arizona Winter School of 2016

## Wintersemester 2019/20

**Selected Topics in Algebra: The Fargues-Fontaine curve**, Johannes Anschütz

## Sommersemester 2019

**Selected Topics in Algebra: Condensed Mathematics**, Peter Scholze**Selected Topics in Algebraic Geometry: Topics about rational points on varieties**, Diego Izquierdo- Course website with exercises (archived link)
- Yifan “Irrational Point” Wu's lecture notes (moved here)
- My notes (incomplete): pdf
**Selected Topics in Topology: Algebraic Curves**, Filip Misev- Course webpage (new link) (archived link)
- My lecture notes: pdf
**Graduate Seminar on Complex Geometry**, René Mboro- Seminar announcement and schedule (archived link)
- I'll probably scan my notes at some point.
**Informal Seminar on Modular Forms**, Matthew Dawes

## Wintersemester 2018/19

**Advanced Algebra I: Local fields and (local) class field theory**, Oliver Bräunling- Course webpage on Bräunling’s website (archived link)
- Exercises on Axel’s website (archived link)
- My lecture notes
**Advanced Topics in Algebraic Geometry: Real differential forms in non-archimedean geometry**, Andreas Mihatsch- Course webpage
- My lecture notes
- Table of contents
- Lectures 1–14 (binder 1): pdf
- Lectures 15–19 (binder 2): pdf
- Lecture 20: pdf
**Advanced Topics in Algebraic Geometry: Jacobians of curves and the Mordell conjecture**, Jens Franke**Algebraic Geometry I**, Georg Oberdieck- Syllabus, exercises and solutions on Matthew Dawes’ webpage (archived link)
- My lecture notes. Please note that in this class I take notes far less detailed than usual, sometimes skipping entire proofs for instance.
**Selected Topics in Algebraic Geometry: Introduction to Mori theory**, Luca Tasin- Course webpage (archived link)
- My lecture notes
- Table of contents
- Lectures 1–12: pdf
- Table of contents: pdf
- Some notes for the exam: pdf
**Graduate Seminar in Advanced Algebra: Diophantine equations in primes**, Alisa Sedunova

## Sommersemester 2018

**Advanced Topics in Geometry: Arithmetic Groups**, Bram Petri- Bram’s webpage (archived link)
- Dave Witte Morris: Introduction to Arithmetic Groups
- My lecture notes
- Lectures 1–13: pdf (coloured) · pdf (black and white)
- Lectures 14–22: pdf (coloured) · pdf (black and white)
- Exam: not being able to present the admittedly quite lengthy definition of arithmetic groups guarantees a fail. One is expected to be able to present theorems and prove them (in case they were proven in class) and give examples for various properties.
**Algebraic Geometry II***(aka Locally Ringed Spaces II)*, Jens Franke- Lecture notes by Ferdinand Wagner
- Exercises on Franke’s webpage
- Bastiaan Cnossen’s notes: lecture notes (black and white), summary (black and white)
**Selected Topics in Algebra: Analytic Number Theory**, Alisa Sedunova- Lecture notes and homework distributed via email
- Sedunova’s webpage (archived link)
**Selected Topics in Algebra: Interactions between Analytic Number Theory and Arithmetic Geometry – Counting rational points on algebraic varieties**, Kevin Destagnol- My lecture notes: pdf
**Selected Topics in Algebra: Homological Methods in Commutative Algebra**, Jens Franke- Lecture notes by Ferdinand Wagner
- Bastiaan Cnossen’s notes: lecture notes (black and white), summary (coloured)
**Topology II**, Irakli Patchkoria- Exercises on Patchkoria’s webpage (archived link)
- My lecture notes
- Lectures 1–11: djvu · pdf
- Lectures 12–15: pdf (coloured) · pdf (black and white)
- Lectures 16–17: pdf (coloured)
- Lectures 18–21: pdf (coloured) (yes, this file does contain an empty page and yes, page numbering is missing from the notes of lecture 21) – Hurewicz theorem
- My notes on the proof of the Hurewicz theorem; essentially the same as above.
- Lectures 22–23: pdf (coloured)
- Lecture 24: pdf (coloured) (this won’t be on the first exam)
- Lecture 25: compact-open topology, suspension-loop adjunction and replacing maps by fibration, cf. e.g. tom Dieck: Algebraic Topology. (This also won’t be on the first exam.)

## Wintersemester 2017/18

**Advanced Algebra I: Algebraic Number Theory**, Yichao Tian- Tian’s notes covering about the first two thirds of the material (new link)
- Tian’s notes on Tate’s thesis (if you need this, I have a copy)
- Felix Schremmer’s notes
- Exercises on Johannes Anschütz’s webpage (archived link)
- My lecture notes: first part (pdf), second part (pdf), course outline
**Algebra II: Introduction to Algebraic Geometry**, Jens Franke**Algebraic Geometry I***(aka Locally Ringed Spaces I)*, Jens Franke**Global Analysis I**, Bram Mesland- Bram’s notes summarising the material (not including the lecture Thorben gave on flows and the ODE solution existence and uniqueness theorem)
- Felix Schremmer’s notes
- Exercises on Bram’s webpage (updated link) (archived link)
- My lecture notes: pdf
**Topology I**, Stefan Schwede- Felix Schremmer’s notes
- Exercises on Schwede’s webpage
- My lecture notes on cohomology, lectures 24–27: djvu pdf

## Miscellany

This is a collection of other stuff: lectures I did not attend but which seem interesting, books or lecture notes I should probably read at some point etc.- Arbeitsgruppe Arithmetische Algebraische Geometrie, Veranstaltungen vorheriger Semester
- Yichao Tian: Introduction to Rigid Geometry (lecture notes for an Advanced Topics in Algebraic Geometry course) (if you need this, I have a copy)
- Yichao Tian: Intersection Theory (lecture notes for a Selected Topics in Algebraic Geometry course)
- Algebraic Geometry I (archived link) as taught by Peter Scholze, notes by Jack Davies
- Algebraic Geometry II (archived link) as taught by Peter Scholze, notes by Jack Davies
- Algebraic Geometry I (archived link) as taught by Daniel Huybrechts, please try to refrain from crying out in horror upon looking at the reflex test
- Algebraic Geometry II (archived link) as taught by Daniel Huybrechts; participants of Franke’s lectures are welcome to stand in awe when reading through the list of basic questions for the exam
- Einführende Algebra-Vorlesungen ab WS 2017/18
- Bastiaan Cnossen’s notes for Algebraic Topology II (Prof. Bödigheimer, SS 2018): lecture notes, overview
- Pieter Belmans: Hochschild (Co)Homology (lecture notes for an Advanced Topics in Algebra course)