7 papers
The complexity of root-finding in orders
Pim Spelier
Given an order, a commutative ring whose additive group is free of finite rank, a natural computational question is whether a fixed univariate polynomial has…
The complexity of intersecting subproducts with subgroups in Cartesian powers
Pim Spelier
Given a finite abelian group and , there are two natural types of subsets of the Cartesian power ; namely, Cartesian powers where is a subset of…
Logarithmic cohomological field theories
David Holmes, Pim Spelier
We introduce a new logarithmic structure on the moduli stack of stable curves, admitting logarithmic gluing maps. Using this we define cohomological field theories taking values in…
Local heights on hyperelliptic curves and quadratic Chabauty
L. Alexander Betts, Juanita Duque-Rosero, Sachi Hashimoto +1
Quadratic Chabauty is a -adic method for determining rational points on curves. Local heights are arithmetic invariants used in the quadratic Chabauty method. We present an algo…
Splitting formulas for the logarithmic double ramification cycle
Pim Spelier
The logarithmic double ramification cycle is roughly a logarithmic Gromov--Witten invariant of . For classical Gromov--Witten invariants, formulas for the pullback al…
Logarithmic tautological rings of the moduli spaces of curves
Rahul Pandharipande, Dhruv Ranganathan, Johannes Schmitt +1
We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes…