1
vote
0answers
142 views

Hodge modules and Deligne-Beilinson cohomology of function fields

Let $K$ be a function field over complex numbers i.e. the fraction field of a complex variety. Then one can define the Deligne-Beilinson cohomology and mixed Hodge modules for $K$ as the direct limit ...
6
votes
0answers
182 views

The Rappoport-Zink spectral sequence vs. the one of the complement of a normal crossing divisor

As far as I understand these matters, for a regular $\mathfrak{X}$ that is proper flat of finite type over $\operatorname{Spec}\mathbb{Z}_p$, the Rappoport-Zink spectral sequence relates the etale ...
16
votes
3answers
2k views

Vanishing cycles in a nutshell?

To quote one source among many, "the general reference for vanishing cycles is [SGA 7] XIII and XV". Is there a more direct way to learn the main principles of this theory (i.e. without the language ...