Torsion in differentials and Berger’s conjecture

Formal Finiteness and the Torsion Conjecture

One denotes by S(d) the collection of all torsion primes of degree d. The well known strong uniform boundedness conjecture states that for every d, the set S(d) is nite. The main results of [KaMa-92] summarize as follows: for all d, S(d) is of density zero, and for d 8, S(d) is nite. It should be mentioned that the original conjecture is not restricted to prime levels, but in [KaMa-92] it is sh...

Organismal Differentials and Organ Differentials.

Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture

We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel’s theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of stable curves, and show how this construction can be applied to clarify a delicate point in Kontsevich’s proof of Witten’s conjecture.

Torsion in Rank 1 Drinfeld Modules and the Uniform Boundedness Conjecture

It is conjectured that for fixed A, r ≥ 1, and d ≥ 1, there is a uniform bound on the size of the torsion submodule of a Drinfeld A-module of rank r over a degree d extension L of the fraction field K of A. We verify the conjecture for r = 1, and more generally for Drinfeld modules having potential good reduction at some prime above a specified prime of K. Moreover, we show that within an L-iso...

Some H1f-groups with Unbounded Torsion and a Conjecture of Kropholler and Mislin

Kropholler and Mislin conjectured that groups acting admissibly on a finite-dimensional G-CW-complex with finite stabilisers admit a finitedimensional model for EFG, the classifying space for proper actions. This conjecture is known to hold for groups with bounded torsion. In this note we consider a large class of groups U containing the above and many known examples with unbounded torsion. We ...