Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / / David Joseph Carchedi.
"We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of point...
Saved in:
Superior document: | Memoirs of the American Mathematical Society, Volume 264, Number 1282 |
---|---|
VerfasserIn: | |
Place / Publishing House: | Providence, RI : : American Mathematical Society,, 2020. |
Year of Publication: | 2020 |
Language: | English |
Series: | Memoirs of the American Mathematical Society ;
Volume 264, Number 1282. |
Online Access: | |
Physical Description: | 1 online resource (132 pages). |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
5006195971 |
---|---|
ctrlnum |
(MiAaPQ)5006195971 (Au-PeEL)EBL6195971 (OCoLC)1153270572 |
collection |
bib_alma |
record_format |
marc |
spelling |
Carchedi, David Joseph, author. Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi. Providence, RI : American Mathematical Society, 2020. 1 online resource (132 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier Memoirs of the American Mathematical Society, 0065-9266 ; Volume 264, Number 1282 Includes bibliographical references. "We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well"-- Provided by publisher. Description based on print version record. Electronic reproduction. Ann Arbor, MI : ProQuest, 2018. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. Algebraic geometry -- Families, fibrations -- Stacks and moduli problems. msc Toposes. Orbifolds. Categories (Mathematics) Electronic books. Print version: Carchedi, David Joseph. Higher orbifolds and deligne-mumford stacks as structured infinity-topoi. Providence, Rhode Island ; American Mathematical Society [2020] 132 pages 9781470441449 (DLC) 2020024075 ProQuest (Firm) Memoirs of the American Mathematical Society ; Volume 264, Number 1282. https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6195971 Click to View |
language |
English |
format |
eBook |
author |
Carchedi, David Joseph, |
spellingShingle |
Carchedi, David Joseph, Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / Memoirs of the American Mathematical Society, |
author_facet |
Carchedi, David Joseph, |
author_variant |
d j c dj djc |
author_role |
VerfasserIn |
author_sort |
Carchedi, David Joseph, |
title |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / |
title_full |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi. |
title_fullStr |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi. |
title_full_unstemmed |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi. |
title_auth |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / |
title_new |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / |
title_sort |
higher orbifolds and deligne-mumford stacks as structured infinity-topoi / |
series |
Memoirs of the American Mathematical Society, |
series2 |
Memoirs of the American Mathematical Society, |
publisher |
American Mathematical Society, |
publishDate |
2020 |
physical |
1 online resource (132 pages). |
isbn |
9781470458102 (e-book) 9781470441449 |
issn |
0065-9266 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA169 |
callnumber-sort |
QA 3169 C373 42020 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6195971 |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516/.07 |
dewey-sort |
3516 17 |
dewey-raw |
516/.07 |
dewey-search |
516/.07 |
oclc_num |
1153270572 |
work_keys_str_mv |
AT carchedidavidjoseph higherorbifoldsanddelignemumfordstacksasstructuredinfinitytopoi |
status_str |
n |
ids_txt_mv |
(MiAaPQ)5006195971 (Au-PeEL)EBL6195971 (OCoLC)1153270572 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Memoirs of the American Mathematical Society, Volume 264, Number 1282 |
hierarchy_sequence |
Volume 264, Number 1282. |
is_hierarchy_title |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / |
container_title |
Memoirs of the American Mathematical Society, Volume 264, Number 1282 |
_version_ |
1792331019653742592 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03338nam a2200445 i 4500</leader><controlfield tag="001">5006195971</controlfield><controlfield tag="003">MiAaPQ</controlfield><controlfield tag="005">20200810211351.0</controlfield><controlfield tag="006">m o d | </controlfield><controlfield tag="007">cr cnu||||||||</controlfield><controlfield tag="008">200810s2020 riu ob 000 0 eng </controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781470441449 </subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781470458102 (e-book)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(MiAaPQ)5006195971</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(Au-PeEL)EBL6195971</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1153270572</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">MiAaPQ</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">MiAaPQ</subfield><subfield code="d">MiAaPQ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA169</subfield><subfield code="b">.C373 2020</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516/.07</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Carchedi, David Joseph,</subfield><subfield code="e">author.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Higher orbifolds and deligne-mumford stacks as structured infinity-topoi /</subfield><subfield code="c">David Joseph Carchedi.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI :</subfield><subfield code="b">American Mathematical Society,</subfield><subfield code="c">2020.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (132 pages).</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Memoirs of the American Mathematical Society,</subfield><subfield code="x">0065-9266 ;</subfield><subfield code="v">Volume 264, Number 1282</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well"--</subfield><subfield code="c">Provided by publisher.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on print version record.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, MI : ProQuest, 2018. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebraic geometry -- Families, fibrations -- Stacks and moduli problems.</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Toposes.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Orbifolds.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Categories (Mathematics)</subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Carchedi, David Joseph.</subfield><subfield code="t">Higher orbifolds and deligne-mumford stacks as structured infinity-topoi.</subfield><subfield code="d">Providence, Rhode Island ; American Mathematical Society [2020]</subfield><subfield code="h">132 pages </subfield><subfield code="z">9781470441449 </subfield><subfield code="w">(DLC) 2020024075 </subfield></datafield><datafield tag="797" ind1="2" ind2=" "><subfield code="a">ProQuest (Firm)</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Memoirs of the American Mathematical Society ;</subfield><subfield code="v">Volume 264, Number 1282.</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6195971</subfield><subfield code="z">Click to View</subfield></datafield></record></collection> |