Year: 2025
Type: preprint
Abstract: Algebraic symplectic cobordism is the universal symplectically oriented cohomology theory for schemes, represented by the motivic commutative ring spectrum MSp constructed by Panin and Walter. The graded algebraic diagonal MSp* of the coefficient ring of MSp is unknown. Through a symplectic version of the Pontryagin-Thom construction, one can associate any symplectic variety X with a symplectic class [X]MSp in MSp-dimX. Still, the problem in using these classes to study the ring MSp* is the paucity of non-trivial examples of symplectic varieties. We modify this construction to obtain elements in MSp* from a large family of varieties that are not symplectic but carry a certain "symplectic twist". Then, using a strategy relying on the Adams spectral sequence for MSp, we find a criterion to select generators among these classes, after taking a completion along the motivic Hopf map.
Source: arXiv (Cornell University)
Author: Gigli, Pietro
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G434337789, G6754795756
OpenAlex ID: W6887708288
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