What is a "discrete spectra" in context of homotopy theory/ derived category theory? It is for example mentioned here. Although it looks quite "googleable" I found nowhere a precise definition. Remark: question is closely related with discussion here: Derived Tensor Product in Terms of Homotopy Groups .
2026-03-25 16:05:17.1774454717
Discrete Spectra
153 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in HOMOTOPY-THEORY
- how to prove this homotopic problem
- Are $[0,1]$ and $(0,1)$ homotopy equivalent?
- two maps are not homotopic equivalent
- the quotien space of $ S^1\times S^1$
- Can $X=SO(n)\setminus\{I_n\}$be homeomorphic to or homotopic equivalent to product of spheres?
- Why do $S^1 \wedge - $ and $Maps(S^1,-)$ form a Quillen adjunction?
- Is $S^{n-1}$ a deformation retract of $S^{n}$ \ {$k$ points}?
- Connection between Mayer-Vietoris and higher dimensional Seifert-Van Kampen Theorems
- Why is the number of exotic spheres equivalent to $S^7,S^{11},S^{15},S^{27}$ equal to perfect numbers?
- Are the maps homotopic?
Related Questions in DERIVED-CATEGORIES
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Images of derived categories of $X, Z$ in derived category of blow up
- derived category of quotient category
- Are quasi-isomorphisms always invertible in the homotopy category?
- Derived functors and induced functors
- Distinguished triangle induced by short exact sequence
- When does the inverse image functor commute with internal hom?
- Derived functor defined with an adapted subcategory
- Ext functor in derived categories
- Serre duality in derived category
Related Questions in SPECTRA
- Reference request: Representability of multiplicative equivariant cohomology theories
- Isomorphism in the case of real symmetric matrices
- Reference for spectra theory (in topology)
- spectrum theory in generalized cohomology
- A question regarding generalized cohomology and spectra : proof of $E^{\ast}(S)\otimes\mathbb{R} = H^{\ast}(S;\pi_{\ast}E\otimes \mathbb{R})$
- Meaning of cocycle on a spectrum?
- Relation of $\mathbb{Z}_2$-cohomology and interger cohomology
- Realizing the Berkovich affine line as a union of Berkovich spectrums
- Definition of the Berkovich spectrum
- Construction of $(p)$-local spectrum.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
In this context, it means a spectrum whose homotopy groups all vanish except possibly for $\pi_0$.
The category of such spectra is equivalent to the category of abelian groups, via $\pi_0$ in one direction, and the Eilenberg-MacLane spectrum functor in the other direction.