algebraic geometry in nLab
Algebraic geometry starts with study of spaces that are locally modeled on (objects in the category) Aff = CRing op {}^{op} – main categories ...
algebraic geometry - contents in nLab
Classical algebraic geometry · algebraic equation, semialgebraic set · maximal spectrum, Zariski topology · locally ringed space · affine ...
Finally, taking the duality between algebra and geometry to the extreme yields notions of noncommutative geometry and/or derived geometry whose ...
Books in algebraic geometry - nLab
1. Introductory level but excellent textbooks 2. Schemes, standard sources David Mumford: Red book of varieties and schemes, Lecture Notes in Mathematics 1358, ...
derived algebraic geometry in nLab
Derived algebraic geometry is the specialization of higher geometry and homotopical algebraic geometry to the (infinity,1)-category of ...
divisor (algebraic geometry) in nLab
In algebraic geometry a divisor (or Weil divisor for definiteness) in a given variety is a formal linear combination of sub-varieties of ...
What non-categorical applications are there of homotopical algebra?
Making algebraic geometry even more geometric (ex: Homological algebra). This actually is a motivation for homological algebra, more than ...
In “2-algebraic geometry” one considers spaces formally dual to 2-rigs, namely to certain tensor categories or more generally to tensor (∞,1)-categories.
Is nLab a good source? : r/math - Reddit
I am learning category theory from Tom Leinster's "Basic Category Theory" (Cambridge University Press, 2014) and have stumbled across nLab while supplementing ...
homotopical algebraic geometry in nLab
Homotopical algebraic geometry is a homotopical generalization of algebraic geometry, where the affine schemes are not necessarily commutative ...
Motivation for the nLab's definition of cohomology?
First, the nLab ... I know what it is taught in good introductory graduate courses on algebraic topology and homological algebra and so on, but ...
Category theory for Algebraic Geometry - MathOverflow
Paolo Aluffi's Algebra Chapter 0 develops abstract algebra using Category theory from the very beginning. The exposition is very clear and ...
How algebraic geometry and motives appears in physics?
Algebraic geometry as such appears because it happens to capture important aspects of the geometry of strings. ... Similarly the target space ...
spectral algebraic geometry in nLab
Spectral algebraic geometry (or maybe E-∞ geometry) is the theory of homotopical algebraic geometry specialized to the (infinity,1)-category of ...
What is the minimum required background to understand articles in ...
The nlab is a convenient (and probably the best) online reference for basic and advanced notions of category theory.
Urs Schreiber on X: "@ncgnl @bardot_cedric Duality between ...
Duality between Geometry and Algebra goes back to Gelfand et al http://ncatlab.org/nlab/show/Gelfand+duality… is the idea behind algebraic ...
Math 632: Algebraic Geometry - Mathematics | U-M LSA
Math 632: Algebraic Geometry. Professor: David E Speyer. Winter 2024 ... Ravi Vakil's blog, the stacks project, the algebraic geometry tag at nLab. I ...
Arithmetic geometry is a branch of algebraic geometry studying schemes (usually of finite type) over the spectrum Spec(Z) of the commutative ...
nLab Migration Done | The n-Category Café - Welcome
... algebraic geometry, n n Lab-wise. I'd like to do that in the slightly more general context that deserves to be called higher geometry. In ...
Noncommutative algebraic geometry - Wikipedia
The methods of noncommutative algebraic geometry are analogs of the methods of commutative algebraic geometry, but frequently the foundations are different.