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6 papers · 2 filters
On descending cohomology geometrically
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal…
Tropical compactification and the Gromov--Witten theory of
Renzo Cavalieri, Hannah Markwig, Dhruv Ranganathan
We use tropical and nonarchimedean geometry to study the moduli space of genus stable maps to relative to two points. This space is exhibited as a tropical compa…
Crepant resolutions and open strings II
Andrea Brini, Renzo Cavalieri
We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of thr…
The distribution of torsion subschemes of abelian varieties
Jeff Achter
We consider the distribution of p-power group schemes among the torsion of abelian varieties over finite fields of characteristic p, as follows. Fix natural numbers g and n, and le…
Irreducibility of Newton strata in GU(1,n-1) Shimura varieties
Jeff Achter
Let L be a quadratic imaginary field, inert at the rational prime p. Fix an integer n at least 3, and let M be the moduli space (in characteristic p) of principally polarized abeli…
Tropicalizing the space of admissible covers
Renzo Cavalieri, Hannah Markwig, Dhruv Ranganathan
We study the relationship between tropical and classical Hurwitz moduli spaces. Following recent work of Abramovich, Caporaso and Payne, we outline a tropicalization for the moduli…