Mindmap on complex analysis in one variable

Monday, November 14th, 2011 | Author:

Here is my mind-map for first-course complex analysis. It contains some well-known theorems and "arrows" between them.

Here it is, and of course you can download it as a PDF or as a SVG (vector graphics) as well (click on the image to enlarge it):

diagrammatic cheat sheet of complex analysis
The license is CC-BY-NC-SA (if you redistribute, put my name on it, don't make profit, share alike).

There are some aspects which require an explanation:

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Properties of Scheme Morphisms

Sunday, November 06th, 2011 | Author:

To prepare for my oral exams in algebraic geometry (covering Hartshorne's book "Algebraic Geometry" Chapter II and III) I sketched an overview diagram of morphism properties in the category of noetherian schemes. Maybe this is a good cheat sheet to keep with you while reading the book for the first or second time (ok, and I dropped a "Nisnevich" for no good reason, you can ignore it).

You can get a PDF version of the image or click on it to get a readable version.

diagrammatic cheat sheet of scheme morphism properties

I'm still in the process of writing down examples and counter-examples to these properties, maybe that list will be online some day (another kind of "counterexamples in algebraic geometry").

As always, I'm happy to hear any comments (did I miss an important arrow, did I get anything wrong) -- but I should stress that the diagram works in Hartshorne-world, not in EGA-terms (this kind of confusion cost me almost one entire day trying to prove wrong statements..)

UPDATE (2011-11-18): improved diagram (more information, less colour) and higher quality PNG file.

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Walk-through to Morel-Voevodsky A¹-homotopy theory part II (page 48, Lemma 1.1)

Wednesday, November 04th, 2009 | Author:

Here is the second part of my walk-through to Voevodskys A¹-homotopy theory:

On page 48, the first Lemma is shown. Without proof - so I will try to illuminate things a little bit by giving the proof. This lemma isn't used until section 3, so you can skip it, if you want to. I suggest not to do so, if you are intimidated by the diagram, because it isn't that hard, and it's a nice exercise to get the concepts in your head right.

Continue reading «Walk-through to Morel-Voevodsky A¹-homotopy theory part II (page 48, Lemma 1.1)»

Category: English, Walkthrough to A1-Homotopy Theory | 5 Comments