# Archive by type

Below are the posts on this blogged sorted into their natural types.

# A computation a day

These posts are largely focused around just computing things, with little focus on background or intuition (outside of any very relevant to the problem).

A Computation a Day: Compactly Supported Cohomology

A Computation a Day: the Brauer Group of a Number Ring

A Computation a Day: a Pullback Pushforward

A Computation a Day: a (Harder) Pullback Pushforward

# Weird examples

These are usually very short posts writing down some sort of example of ‘weird’ behavior. These usually have very little in the way of background and/or intuition.

Weird Example: Pullback of Noetherian is Not Noetherian

Weird Example: Pullback of Very Ample by Finite is not Very Ample

Weird example: finite maps don’t preserve projectivity

# Short blurbs

These are just short posts about something random. Once again, no real intention of discussing background material and/or intuition.

The Nullstellensatz

Topological Genus Agrees with Arithmetic Genus

What Information is Contained in an ‘Infinitesimal Neighborhood’ of a Point?

Classifying One-dimensional Algebraic Groups

Classifying one dimensional groups (II)

Hodge Symmetry in Characteristic Zero

Line Bundles on the Circle

A Class Field Theoretic Phenomenon

Morphisms of a ‘Set Theoretic Nature’

Kummer Theory and the Weak Mordell-Weil Theorem

Maps from Simply Connected Projective Varieties to Curves

# Expositions

These are usually longer posts, usually with the intent of giving an introduction and/or overview of a particular topic. These usually focus on giving sufficiently much background and intuition as to elucidate whatever their subject matter may be.

Etale Cohomology: Motivation

Flat Morphisms and Flatness

Unramified Morphisms

Fundamental of (Abelian) Group Cohomology

Group Schemes and Affine Group Schemes

An Invitation to \$p\$-adic Hodge Theory, or: How I Learned to Stop Worrying and Love Fontaine

Some Examples of Geometric Galois Representations

The Tate Conjecture Over Finite Fields

Algebraic de Rham Cohomology and the Degeneration of the Hodge Spectral Sequence

A Different Viewpoint on Étale Cohomology

$p$-divisible Groups, Formal Groups, and the Serre-Tate Theorem

Local Class Field Theory: a Discussion

Galois Groups of Local and Global Fields

A smattering of representation theory

A ‘brief’ discussion about torsors

The Fontaine-Winterberger theorem: going full tilt

A fun (enough) talk

Some motivation for p-adic Hodge theory

Some notes on automorphic representations

Reductive groups: a rapid introduction

# Shimura varieties

Shimura Varieties: Motivation

The Langlands conjecture and the cohomology of Shimura varieties