PushForward -- methods to compute the pushforward of a module along a ring map

Description

Given a ring map $f \colon A \to B$, and a $B$-module $M$, $M$ has the structure of an $A$-module, and if this module is finitely generated over $A$, the routine pushFwd in this package will compute such an $A$-module. This is also functorial, in that if a map of $B$-modules (both of which are finitely generated over $A$), then pushFwd(RingMap,Matrix) will return the induced map on $A$-modules.

In an algebraic sense, this is really a pull back, but thinking geometrically, the functions here implement the push forward of a module (or sheaf).

This package was originally implemented by Claudiu Raicu, some changes were introduced by Karl Schwede, and later by David Eisenbud and Mike Stillman.

Authors

Version

This documentation describes version 0.6 of PushForward.

Citation

If you have used this package in your research, please cite it as follows:

@misc{PushForwardSource,
  title = {{PushForward: push forwards of finite ring maps. Version~0.6}},
  author = {Claudiu Raicu and David Eisenbud and Mike Stillman},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- isModuleFinite -- see isModuleFinite(RingMap) -- whether the target of a ring map is finitely generated over source
- pushFwd -- push forward
Methods
- isModuleFinite(Ring) -- see isModuleFinite(RingMap) -- whether the target of a ring map is finitely generated over source
- isModuleFinite(RingMap) -- whether the target of a ring map is finitely generated over source
- pushFwd(Ring) -- see pushFwd(RingMap) -- push forward of a finite ring map
- pushFwd(RingMap) -- push forward of a finite ring map
- pushFwd(Matrix) -- see pushFwd(RingMap,Matrix) -- push forward of a module map via a finite ring map
- pushFwd(RingMap,Matrix) -- push forward of a module map via a finite ring map
- pushFwd(Module) -- see pushFwd(RingMap,Module) -- push forward of a module via a finite ring map
- pushFwd(RingMap,Module) -- push forward of a module via a finite ring map
Symbols
- NoPrune -- NoPrune option for pushFwd

For the programmer

The object PushForward is a package, defined in PushForward.m2.

The source of this document is in PushForward.m2:304:0.