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...

{\displaystyle S\to \operatorname {Spec} \mathbb {Z} } . The smooth base change theorem states the following: let f : X → S {\displaystyle f:X\to S} be a...

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...

These kinds of theorems lead to one of the deepest theorems about the cohomology of algebraic varieties, the decomposition theorem, paving the path...

{\displaystyle f^{!}} , unless f {\displaystyle f} is also proper. Proper base change theorem "Section 26.24 (01LA): Functoriality for quasi-coherent modules—The...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

representability, see Neeman 1996 van den Bergh, Michel (September 1997). "Existence Theorems for Dualizing Complexes over Non-commutative Graded and Filtered Rings"...

∗ ⇆ f ∗ {\displaystyle f^{*}\leftrightarrows f_{*}} ( R ) f ! ⇆ ( R ) f ! {\displaystyle (R)f_{!}\leftrightarrows (R)f^{!}} Base change theorems v t e...

of perverse sheaves. Another useful property of the image functors is base change. Given continuous maps f : X → Z {\displaystyle f:X\rightarrow Z} and...

2022-09-25. Schnürer, Olaf M.; Soergel, Wolfgang (2016-05-19). "Proper base change for separated locally proper maps". Rendiconti del Seminario Matematico...

subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or loge(x). In analytic number theory, Mertens' theorems are three...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

support. Its existence follows from certain properties of Rf! and general theorems about existence of adjoint functors, as does the unicity. The notation...

appeared in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously derived no free lunch theorems for machine learning (statistical...

envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters...

by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to...

is the change in linear momentum from time t1 to t2. This is often called the impulse–momentum theorem (analogous to the work–energy theorem). As a result...

The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the...

Shahshahani Prize Winners: 1.Amnon Neeman, An improvement on the base-change theorem and the functor f^!, Bull. Iran. Math. Soc. (2023) 49:25. 2. Peter...

_{a}^{b}g(x)\,dx.} There are various slightly different theorems called the second mean value theorem for definite integrals. A commonly found version is...

Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with...

The two versions are based on the two Kirchhoff's circuit laws. Miller theorems are not only pure mathematical expressions. These arrangements explain...

pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The category of schemes is a broad setting...

one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance...

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

notation does not suffice for the purposes of Goodstein's theorem. To achieve the ordinary base-n notation, where n is a natural number greater than 1,...

(OEIS: A050920) Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number. 294001...

In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function...

which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to...

order. The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate. From A, draw a line...