The derived moduli stack of shifted symplectic structures
Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 221-241.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

We introduce and study the derived moduli stack 𝐒𝐲𝐦𝐩(X,n) of n-shifted symplectic structures on a given derived stack X, as introduced in [8]. In particular, under reasonable assumptions on X, we prove that 𝐒𝐲𝐦𝐩(X,n) carries a canonical quadratic form, in the sense of [14]. This generalizes a classical result of Fricke and Habermann (see [13]), which was established in the C -setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated in [14].

Publié le :
DOI : 10.4171/RSMUP/24
Classification : 14, 53
Mots clés : Derived algebraic geometry, moduli spaces, Lie algebroids, shifted symplectic structures
Bach, Samuel 1 ; Melani, Valerio 2

1 University of British Columbia, Vancouver, Canada
2 Università di Pisa, Italy and Università di Milano, Italy
@article{RSMUP_2019__141__221_0,
     author = {Bach, Samuel and Melani, Valerio},
     title = {The derived moduli stack of shifted symplectic structures},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {221--241},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {141},
     year = {2019},
     doi = {10.4171/RSMUP/24},
     mrnumber = {3962830},
     zbl = {1436.14005},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/24/}
}
TY  - JOUR
AU  - Bach, Samuel
AU  - Melani, Valerio
TI  - The derived moduli stack of shifted symplectic structures
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2019
SP  - 221
EP  - 241
VL  - 141
PB  - European Mathematical Society Publishing House
PP  - Zuerich, Switzerland
UR  - http://www.numdam.org/articles/10.4171/RSMUP/24/
DO  - 10.4171/RSMUP/24
ID  - RSMUP_2019__141__221_0
ER  - 
%0 Journal Article
%A Bach, Samuel
%A Melani, Valerio
%T The derived moduli stack of shifted symplectic structures
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2019
%P 221-241
%V 141
%I European Mathematical Society Publishing House
%C Zuerich, Switzerland
%U http://www.numdam.org/articles/10.4171/RSMUP/24/
%R 10.4171/RSMUP/24
%F RSMUP_2019__141__221_0
Bach, Samuel; Melani, Valerio. The derived moduli stack of shifted symplectic structures. Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 221-241. doi : 10.4171/RSMUP/24. http://www.numdam.org/articles/10.4171/RSMUP/24/

Cité par Sources :