4 papers
There is no Definable Grauert Direct Image Theorem
Hélène Esnault, Moritz Kerz
We prove the claim in the title by showing that a definable Grauert Direct Image Theorem in o-minimal geometry would imply a weak representability-like property of the definable Pi…
A non-abelian version of Deligne's Fixed Part Theorem
Hélène Esnault, Moritz Kerz
We formulate and prove a non-abelian analog of Deligne's Fixed Part theorem on Hodge classes, revisiting previous work of Jost--Zuo, Katzarkov--Pantev and Landesman--Litt. To this…
Semistable Lefschetz Pencils
Hélène Esnault, Moritz Kerz
We study the geometry and cohomology of Lefschetz pencils for semistable schemes over a discrete valuation ring. We relate the global cohomological properties of the Lefschetz penc…
Algebraic flat connections and o-minimality
Hélène Esnault, Moritz Kerz
We prove that an algebraic flat connection has definable flat sections in the analytic exponential structure if and only if it is regular singular with unitary monodromy eigenvalue…