This website design was stolen (with permission) from Ashwin Iyengar.
Pol van Hoften
I am a second year Ph.D student of the London School of Geometry and Number Theory
and the King's College London math department
. I am interested in various aspects of the Langlands program and its applications to arithmetic. My research is in the (characteristic p) geometry of Shimura varieties and its applications to the Langlands programme such as level lowering congruences, functoriality and the weight-monodromy conjecture for Shimura varieties. Before coming to London, I completed a bachelor's and master's at the University of Utrecht and wrote a thesis on the cohomology of moduli spaces of curves with Professor Carel Faber (available on request).
My e-mail address is Pol dot van_Hoften at kcl dot ac dot uk.
Publications / Preprints
Notes / Miscellaneous
Igusa Varieties & Mantovan's Formula: These are the notes from a talk I gave in the London number theory study group in summer 2019. I briefly review the Newton stratification on the mod p fiber of a PEL type Shimura variety (with good reduction at p) and then introduce Oort's foliation. After giving some background on completely slope divisible Barsotti-Tate groups I define Igusa varieties and prove that they are étale covers of the leaves of the foliation. I end by defining the `product structure' on the Newton strata, which is a finite surjective map from the product of an Igusa variety with a truncated Rapoport-Zink space to a Newton stratum.
Perverse Sheaves and nearby cycles: These are the notes from a talk I gave in the London number theory study group in fall 2018. I introduce the triangulated category of l-adic sheaves with constructible cohomology and discuss the six functor formalism in this context. I then define the perverse t-structure and talk about the intermediate extension functor. In the last section I discuss Milnor fibers, nearby cycles and discuss the fact that nearby cycles 'preserve perversity'.
Perfectoid rings, A_inf, and the pro-étale site: These are the notes from a talk I give in the London number theory study group in summer 2018. The first half follows Section 3 of Bhatt-Morrow-Scholze and the second half is about the pro-étale site of an adic space (notes by James Newton).
Classical Motives: These are the notes from a talk I gave in the London number theory study group in spring 2018. I start by giving a quick introduction to intersection theory and then define various categories of Chow motives. I end by discussing the proof of Theorem 1 of Jannsen's paper Motives, numerical equivalence, and semi-simplicity.
Barsotti-Tate groups: These are the notes from a talk I gave in the junior number theory seminar in 2018.
Mixed Complexes: These are the notes from a talk I gave in the seminar on perverse sheaves in the spring of 2017 in Nijmegen. I introduce the notion of weight for an l-adic sheaf and define pure and mixed sheaves. I then discuss the derived category of such mixed sheaves and its stability properties under the six operations. I end by proving Proposition 5.12 of Beilinson-Bernstein-Deligne.
Descent of Morphisms: These are the notes from a talk I gave for topics in algebraic geometry in spring 2016 in Leiden.