5 papers · 1 filter
Murphy's law in non-abelian Hodge theory
Gregorio Baldi, Yeuk Hay Joshua Lam
We construct explicit examples of non-integral variations of -Hodge structures. Our approach leverages Fenchel--Nielsen-type parameterizations, due to Kabaya and Maskit…
p-Curvature and Non-Abelian Cohomology
Yeuk Hay Joshua Lam, Daniel Litt
Let be a smooth projective morphism. Katz proved the Grothendieck-Katz -curvature conjecture for the Gauss-Manin connection on the -th cohomology of : if its $p…
Local systems which do not come from abelian varieties
Paul Brommer-Wierig, Yeuk Hay Joshua Lam
For each smooth curve over a finite field, after puncturing it at finitely many points, we construct local systems on it of geometric origin which do not come from a family of abel…
Algebraicity and integrality of solutions to differential equations
Yeuk Hay Joshua Lam, Daniel Litt
We formulate a conjecture classifying algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the primes appearing in the denominators of the coe…
On the locus of curves mapping to a fixed target
Yeuk Hay Joshua Lam, Federico Moretti, Giovanni Passeri
Suppose is a smooth variety equipped with a top form. We prove a simple theorem giving a sharp lower bound on the geometric genus of a family of subvarieties of , in terms o…