Richard Pink

Finite subgroups of algebraic groups

Generalizing a classical theorem of Jordan to arbitrary characteristic, we prove that every finite subgroup of GLn over a field of any characteristic p possesses a subgroup of bounded index which is composed of finite simple groups of Lie type in characteristic p, a commutative group of order prime to p, and a p-group. While this statement can be deduced from the classification of finite simple groups, our proof is self-contained and uses methods only from algebraic geometry and the theory of linear algebraic groups. We believe that our results can serve as a viable substitute for classification in a range of applications in various areas of mathematics.

A Combination of the Conjectures of Mordell-Lang and André-Oort

We propose a conjecture combining the Mordell-Lang conjecture with an important special case of the Andre-Oort conjecture, and explain how existing results imply evidence for it.

On -invariant subvarieties of semiabelian varieties and the Manin-Mumford conjecture

Let A be a semiabelian variety over an algebraically closed field of arbitrary characteristic, endowed with a finite morphism ψ : A → A. In this paper we give an essentially complete classification of all ψ-invariant subvarieties of A. For example, under some mild assumptions on (A,ψ) we prove that every ψinvariant subvariety is a finite union of translates of semiabelian subvarieties. This result is then used to prove the Manin-Mumford conjecture in arbitrary characteristic and in full generality. Previously, it had been known only for the group of torsion points of order prime to the characteristic of K. The proofs involve only algebraic geometry, though scheme theory and some arithmetic arguments cannot be avoided.

Vector bundles with a Frobenius structure on the punctured unit disc

Let

Euler-Poincaré formula in equal characteristic under ordinariness assumptions

\mathbb{C}

A connectedness criterion for ℓ-adic galois representations-adic galois representations

be a complete non-archimedean-valued algebraically closed field of characteristic p > 0 and consider the punctured unit disc

Monodromy Groups Associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic

\dot{D} \subset \mathbb{C}

A note on pseudo-CM representations and differential Galois groups

. Let q be a power of p and consider the arithmetic Frobenius automorphism

Compactification of a Drinfeld period domain over a finite field

\sigma_{\dot{D}}: x \mapsto x^{q^{-1}}

Kummer theory for Drinfeld modules

. A