This is called "Stackification via torsors" in the book by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche and Andrew Kresch. See Andrew Kresch's homepage:

http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1

more specifically chapter 4, \S 4.

http://www.math.uzh.ch/index.php?file&key1=5161

For sure, this is done in the stacks project

http://stacks.math.columbia.edu/

but I couldn't find the exact reference (probably the keyword is: quotient stack).

For a more historical point of view, see also the related question Algebraic stacks as (étale) groupoid algebraic spaces/schemes .

This is called "Stackification via torsors" in the book by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche and Andrew Kresch. See Andrew Kresch's homepage:

http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1

more specifically chapter 4, \S 4.

http://www.math.uzh.ch/index.php?file&key1=5161

For sure, this is done in the stacks project

http://stacks.math.columbia.edu/

but I couldn't find the exact reference (probably the keyword is: quotient stack).

For a more historical point of view, see also the related question Algebraic stacks as (étale) groupoid algebraic spaces/schemes .

This is called "Stackification via torsors" in the book by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche und Andrew Kresch. See Andrew Kresch's homepage:

http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1

more specifically chapter 4, \S 4.

http://www.math.uzh.ch/index.php?file&key1=5161

For sure, this is done in the stacks project

http://stacks.math.columbia.edu/

but I couldn't find the exact reference (probably the keyword is: quotient stack).

For a more historical point of view, see also the related question Algebraic stacks as (étale) groupoid algebraic spaces/schemes .

This is called "Stackification via torsors" in the book by Kai Behrend, Brian Conrad, Dan Edidin, William Fulton, Barbara Fantechi, Lothar Göttsche and Andrew Kresch. See Andrew Kresch's homepage:

http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1

more specifically chapter 4, \S 4.

http://www.math.uzh.ch/index.php?file&key1=5161

For sure, this is done in the stacks project

http://stacks.math.columbia.edu/

but I couldn't find the exact reference (probably the keyword is: quotient stack).

For a more historical point of view, see also the related question Algebraic stacks as (étale) groupoid algebraic spaces/schemes .