Questions tagged [nearby-cycles]

Let $R$ be a Henselian discrete valuation ring. Let $S=\mathrm{Spec} R$ be the corresponding trait, with generic point $\eta$ and closed point $s$. Let $f:X\to S$ be a smooth proper morphism of ...

Let $S$ be the spectrum of a Henselian discrete valuation ring (called a Henselian trait). Let $f:X\to S$ be a finite type, separated morphism of schemes. Let $\eta\in S$ be the generic point. Let $s\...

Let $X$ be a variety over $\mathbb C$. Let $f\colon X \to \mathbb{A}^1$ be a regular function. I understand that there is an analytic nearby cycles functor, defined in terms of the exponential map. I ...

In some famous papers like Gaitsgory's "Construction of central elements in the affine Hecke algebra via nearby cycles" and Beilinson-Bernstein's "A proof of Jantzen conjectures", ...

Let $X$ be a scheme over a henselian trait $S = (S,s,\eta)$. Let $\ell$ be a prime number which is invertible on $S$ and let $\Lambda := \mathbb Z_{\ell}/\ell^k\mathbb Z_{\ell}$ where $k\geq 1$. Let $\...

In the paper Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink by Gil Guibert, Francois Loeser and Michel Merle, the authors defined the morphism for which I ...