Arithmetic geometryRigid geometryModuli spacesComplex algebraic geometryp-adic Hodge theorySingularity theoryLanglands programComputational algebraic geometryAnabelian geometry
MathematicsMathematics
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Notes on talk 1. anabelian geometry: introduction

Ricciflows
Ricciflows

This person is lazy, nothing was left behind...

1. What is contained in “Galois type” data?Gauss: The regular $n$-gon can be constructed by straightedge and compass if and only if $n = 2^{k}p_{1} . . . p_{r}$ where $p_{i} = 2^{2^{n_{i}}} + 1$ are Fermat primes. For example, $n = 17$. (Based on the study of the extension $\mathbb{Q}(\xi_{n})/\mathbb{Q}$ and cyclotomic polynomials). Here the key is that the hidden symmetries are in the Galois group action (not in the geometric symmetry). Later we will consider the “hidden” structures in the abs ...

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2024-08-23 21:21:20
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MathematicsMathematics
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RicciflowsRicciflows
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2 months ago
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An introduction to different branches of mathematics

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The note is mainly a sketch of basic knowledge concerning general topology, differential geometry, functional analysis, algebraic geometry, etc., starting from a discussion of Euclidean spaces. However, there maybe some mistakes in the note, so use at your own risk. For simplicity, some details are omitted and can be found in the references provided. Further materials concerning algebraic geometry, especially arithmetic algebraic geometry, can be referred to another note written by the author, N ...

MathematicsMathematics
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RicciflowsRicciflows
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3 months ago
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Note on arithmetic algebraic geometry

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The note is mainly a summary of basic knowledge that the author learned in arithmetic geometry. One of the aims of this note is to provide a preliminary for Perfectoid geometry. Most contents are fundamental, but they are essential towards Perfectoid geometry. The ultimate goal of this note is to help readers to understand Peter Scholze's classic paper , where the notion of perfectoid spaces first appeared.