4 papers
math.AG2026
On the cohomological purity of the affine Springer fibers
Zongbin Chen
We address questions posed by Gérard Laumon and Jean-Loup Waldspurger concerning the cohomological purity of affine Springer fibers. More precisely, we show that an affine Springer…
math.AG2024
Purity of the anisotropic affine Springer fibers for
Zongbin Chen
For the group and the anisotropic elements, we confirm the purity hypothesis of Goresky, Kottwitz and MacPherson, which states that the affine Springer fibers are…
math.AG2024
A decomposition theorem for the affine Springer fibers
Zongbin Chen
According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformati…
math.AG2024
On the dependence of the affine Springer fibers on their root valuation datum
Zongbin Chen
For the group , we confirm a conjecture of Goresky, Kottwitz and MacPherson, which states that the cohomology of the affine Springer fibers depend only on the root…