higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
The derived geometry-version of symplectic geometry.
Tony Pantev, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi, Shifted symplectic structures, Publ. Math. IHES 117:1 (2013) 271–328 arXiv:1111.3209
Damien Calaque, Lagrangian structures on mapping stacks and semi-classical TFTs, arXiv:1306.3235.
Damien Calaque, Three lectures on derived symplectic geometry and topological field theories, 2014,
pdf - see also these notes
Pavel Safronov, Quasi-Hamiltonian reduction via classical Chern–Simons theory, arXiv:1311.6429
James Wallbridge, Derived smooth stacks and prequantum categories, arxiv/1610.00441
Xiaojun Chen, Farkhod Eshmatov, Calabi-Yau algebras and the shifted noncommutative symplectic structure, arXiv:1802.07423
Chris Brav, Vittoria Bussi, Dominic Joyce, A Darboux theorem for derived schemes with shifted symplectic structure, 2013, arXiv:1305.6302.
Oren Ben-Bassat, Christopher Brav, Vittoria Bussi, Dominic Joyce, A ‘Darboux Theorem’ for shifted symplectic structures on derived Artin stacks, with applications, arXiv:1312.0090
Pavel Safronov, Dominic Joyce, A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes, arXiv:1506.04024
Shifted Poisson structures
Damien Calaque, Tony Pantev, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi, Shifted Poisson structures and deformation quantization, Journal of topology 10.2 (2017) 483–584 arXiv:1506.03699
Valerio Melani, Poisson bivectors and Poisson brackets on affine derived stacks, arXiv:1409.1863
J. P. Pridham, Shifted Poisson and symplectic structures on derived N-stacks, arXiv:1504.01940
J. P. Pridham, Shifted bisymplectic and double Poisson structures on noncommutative derived prestacks, arXiv:2008.11698
J. P. Pridham, Shifted symplectic structures on derived analytic moduli of l-adic local systems and Galois representations, arXiv:2205.02292
Pavel Safronov, Poisson reduction as a coisotropic intersection, arXiv:1509.08081
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Last revised on October 30, 2023 at 08:27:09. See the history of this page for a list of all contributions to it.