74 research outputs found
Curves with only triple ramification
I show that the set of smooth curves of genus g admitting branched coverings
X->P^1 with only triple ramification points has dimension at least max(2g-3,g).
In characteristic two, such curves have tame rational functions and an analog
of Belyi's Theorem applies to them.Comment: 12 pages, section on semistable reduction extended, otherwise minor
changes, to appear in Ann. Inst. Fourie
Komplexe Analysis - Algebraicity and Transcendence (hybrid meeting)
This is the report of the Oberwolfach workshop Komplexe Analysis 2020. It was mainly devoted to the transcendental methods of complex algebraic geometry and featured eighteen talks about recent important developments in Hodge theory, moduli spaces, hyperbolicity, Fano varieties, algebraic foliations, algebraicity theorems for subvarieties and their applications to transcendence proofs for numbers. Two talks were more algebraic in nature and devoted to non-commutative deformations and syzygies of secant varieties
The six functors for Zariski-constructible sheaves in rigid geometry
We prove a generic smoothness result in rigid analytic geometry over a characteristic zero nonarchimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well-adapted to "spreading out" arguments, in analogy with the use of generic points in scheme theory. As an application, we develop a six functor formalism for Zariski-constructible \'etale sheaves on characteristic zero rigid spaces. Among other things, this implies that characteristic zero rigid spaces support a well-behaved theory of perverse sheaves
- …