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Does it exist online and where can one find it? (For example, these two sources are not official; is the longer one complete?)

This is not a complete reference of course, but there is Lecture 26 (Ring Schemes; The Witt Scheme) in Mumford's book Lectures on curves on an algebraic surface

Perhaps, one could define the "entangledness" of an open curve (of unit lenghth and parametrized in arclength) as the minimum $$\mathrm{min}_{H}\;E(H), $$ over all possible smooth simple "strighten …

Let $V$ be an $n$-dimensional real vector space, $\Lambda\subseteq V$ a lattice, and $K$ a subgroup of $Aut_{\mathbb{Z}}(\Lambda)\cong GL(n,\mathbb{Z})$. Let also $\sigma \in Z^1(K,V/\Lambda)$, $\sigm …

M. Nakahara, Geometry, topology and physics. Paragraph 10.5 "Gauge theories", specifically 10.5.1 "$U(1)$ gauge theories". R.S. Palais, The geometrization of physics, lecture notes from a course at N …

If a mathematician who doesn't know much about the physicist's jargon and conventions had the curiosity to learn how the so called Standard Model (of particle physics, including SUSY) works, where sho …

I'm aware of the existence of complete (abstract) algebraic varieties that are not projective but, probably due to my ignorance, I have the impression that they arise only as very particular examples …

In this interview by Eric Weinstein to Roger Penrose, Timestamp 1:24:05., what result is the host talking about? Transcription of the relevant part: "If you have two sets of symmetries, known as Lie …

Let $T=(\mathbb{C}^*)^n$ act on $\mathbb{P}^n$ torically by $$t.[x_0:\dots:x_n]=[x_0\;:\;t_1x_1\;:\;\ldots \;:\;t_nx_n]$$ I would like to know an expression for the equivariant Chern character $\ma …

In an answer to this MO question [link] Fernando Muro sais: the mapping cone of a morphism in a triangulated category is unique up to non-unique isomorphism. This fact has originated a lot of re …

As far as I read (See page 138 of R.W.Sharpe), the Erlangen program, strictly speaking, describes connected homogeneus manifolds $X$ as $G/H$ where $G$ is a Lie group considered as the "automorphism g …

The goal of this question is to recall a certain mathematical fact -not in my field- that I was once briefly told and that I have fogotten, and also to collect similar results. The fact, I think, wa …

I've been asked some questions by a friend interested in crystallography, and the following questions (I'm not an expert) came spontaneous to me: 1) Are there two finite subgroups $P,P'\subset\mat …

I have heard stated the following Theorem. If $\Sigma$ is a (orientable) surface, then $\mathrm b_1(\Sigma)$ counts the maximum number of "circular cuts" (embedded circles $C_1,\ldots,C_m$) that you …

I've stumbled upon the statement that the morphism $\pi$ from a root stack of the form $\sqrt[r]{\mathscr{L}/\mathscr{Y}}$ (i.e. the "generic" version, not the one concentrated along a divisor) to its …