Locally Complete Intersection Maps and the Proxy Small Property

Briggs B, Iyengar SB, Letz JC, Pollitz J (2021)
International Mathematics Research Notices.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Briggs, Benjamin; Iyengar, Srikanth B; Letz, Janina CarmenUniBi ; Pollitz, Josh
Abstract / Bemerkung
It is proved that a map φ:R→S of commutative Noetherian rings that is essentially of finite type and flat is locally complete intersection if and only if S is proxy small as a bimodule. This means that the thick subcategory generated by S as a module over the enveloping algebra S⊗RS contains a perfect complex supported fully on the diagonal ideal. This is in the spirit of the classical result that φ is smooth if and only if S is small as a bimodule; that is to say, it is itself equivalent to a perfect complex. The geometric analogue, dealing with maps between schemes, is also established. Applications include simpler proofs of factorization theorems for locally complete intersection maps.
Erscheinungsjahr
2021
Zeitschriftentitel
International Mathematics Research Notices
ISSN
1073-7928
eISSN
1687-0247
Page URI
https://pub.uni-bielefeld.de/record/2956738

Zitieren

Briggs B, Iyengar SB, Letz JC, Pollitz J. Locally Complete Intersection Maps and the Proxy Small Property. International Mathematics Research Notices. 2021.
Briggs, B., Iyengar, S. B., Letz, J. C., & Pollitz, J. (2021). Locally Complete Intersection Maps and the Proxy Small Property. International Mathematics Research Notices. https://doi.org/10.1093/imrn/rnab041
Briggs, B., Iyengar, S. B., Letz, J. C., and Pollitz, J. (2021). Locally Complete Intersection Maps and the Proxy Small Property. International Mathematics Research Notices.
Briggs, B., et al., 2021. Locally Complete Intersection Maps and the Proxy Small Property. International Mathematics Research Notices.
B. Briggs, et al., “Locally Complete Intersection Maps and the Proxy Small Property”, International Mathematics Research Notices, 2021.
Briggs, B., Iyengar, S.B., Letz, J.C., Pollitz, J.: Locally Complete Intersection Maps and the Proxy Small Property. International Mathematics Research Notices. (2021).
Briggs, Benjamin, Iyengar, Srikanth B, Letz, Janina Carmen, and Pollitz, Josh. “Locally Complete Intersection Maps and the Proxy Small Property”. International Mathematics Research Notices (2021).

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Suchen in

Google Scholar