Relate the direct image and the pull-back of sheaves
In mathematics, the base change theorems relate the direct image and the inverse image of sheaves. More precisely, they are about the base change map, given by the following natural transformation of sheaves:
where
is a Cartesian square of topological spaces and is a sheaf on X.
Such theorems exist in different branches of geometry: for (essentially arbitrary) topological spaces and proper maps f, in algebraic geometry for (quasi-)coherent sheaves and f proper or g flat, similarly in analytic geometry, but also for étale sheaves for f proper or g smooth.
and 20 Related for: Base change theorems information
mathematics, the basechangetheorems relate the direct image and the inverse image of sheaves. More precisely, they are about the basechange map, given by...
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...
{\displaystyle f^{!}} , unless f {\displaystyle f} is also proper. Proper basechangetheorem "Section 26.24 (01LA): Functoriality for quasi-coherent modules—The...
of perverse sheaves. Another useful property of the image functors is basechange. Given continuous maps f : X → Z {\displaystyle f:X\rightarrow Z} and...
∗ ⇆ f ∗ {\displaystyle f^{*}\leftrightarrows f_{*}} ( R ) f ! ⇆ ( R ) f ! {\displaystyle (R)f_{!}\leftrightarrows (R)f^{!}} Basechangetheorems v t e...
2022-09-25. Schnürer, Olaf M.; Soergel, Wolfgang (2016-05-19). "Proper basechange for separated locally proper maps". Rendiconti del Seminario Matematico...
order. The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate. From A, draw a line...
support. Its existence follows from certain properties of Rf! and general theorems about existence of adjoint functors, as does the unicity. The notation...
theorem is an easily stated and easily understood consequence of theorems Wolpert and Macready actually prove. It is weaker than the proven theorems,...
envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters...
representability, see Neeman 1996 van den Bergh, Michel (September 1997). "Existence Theorems for Dualizing Complexes over Non-commutative Graded and Filtered Rings"...
as above. QED There are various slightly different theorems called the second mean value theorem for definite integrals. A commonly found version is...
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...
The two versions are based on the two Kirchhoff's circuit laws. Miller theorems are not only pure mathematical expressions. These arrangements explain...
In database theory, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store can provide...
{\displaystyle S\to \operatorname {Spec} \mathbb {Z} } . The smooth basechangetheorem states the following: let f : X → S {\displaystyle f:X\to S} be a...
images R i f ∗ F {\displaystyle R^{i}f_{*}F} are coherent. Proper basechangetheorem Stein factorization Hartshorne (1977), Appendix B, Example 3.4.1...
reasonable assumptions about the noise in the underlying hardware. Threshold theorems for classical computation have the same form as above, except for classical...
_{b}(x)\end{aligned}}} This completes the derivation. To state the change of base logarithm formula formally: ∀ a , b ∈ R + , a , b ≠ 1 , ∀ x ∈ R + ,...
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...
Global Information
