My master’s thesis. Introduces the language needed for Serre’s Tor-formula and proves its main theorem.
Math Writing
Introduces Grothendieck spectral sequences and proves their existence, followed by two examples: base-change for Tor and Ext.
Proves the existence of the dual isogeny to an isogeny of two elliptic curves, then establishes some of its basic properties.
Introduces simplicial approximation, then uses barycentric subdivision and generalized barycentric subdivision to prove the general simplicial approximation theorem.
Covers Čech cohomology of abelian sheaves on topological spaces with respect to a given open covering. The main result: Čech cohomology and regular cohomology of quasi-coherent sheaves on noetherian separated schemes coincide.
My bachelor’s thesis. Proves Grothendieck’s vanishing theorem for sheaf cohomology on noetherian topological spaces.
Introduces adjunctions in category theory. Three equivalent definitions are given, with an excursus on reflective subcategories.
Explains and proves the Banach–Tarski paradox, along with similar, easier paradoxes like the Sierpiński–Mazurkiewicz paradox and the Hausdorff paradox.
Discusses the properties of determinants on free modules of finite rank over a commutative ring.