3 papers
math.NT2026
A de Rham weight part of Serre's conjecture and generalized mod BGG decompositions
Martin Ortiz
We propose the use of de Rham cohomology of special fibers of Shimura varieties to formulate a geometric version of the weight part of Serre's conjecture. We conjecture that this f…
math.NT2026
Theta operators on Hodge type Shimura varieties
Martin Ortiz
We construct a new family of mod weight shifting differential operators on Hodge type Shimura varieties at hyperspecial level. First we construct basic theta operators, labelle…
math.DS2019
Boundedness of Fatou components of the family f(z)=λsin(z)+a
F. R. Martinez, G. Sienra
In this paper we discuss the boundedness of the Fatou components for the sine family and the extended sine family, mainly when the parameter λhas modulus greater than 1 and the map…