14 citations · 67 across the 13 of their papers we have counts for
14 papers
Infinitely many primes of basic reduction for some abelian fourfolds
Wanlin Li, Elena Mantovan, Rachel Pries +1
If is an elliptic curve, defined over or a number field having at least one real embedding, then Elkies proved that has supersingular reduction at infinitely m…
Positive density of primes of ordinary reduction for abelian varieties of simple signature
Victoria Cantoral Farfán, Wanlin Li, Elena Mantovan +2
By a result of Serre, if is an elliptic curve without CM defined over a number field , then the set of primes of for which has ordinary reduction has density . Ka…
On knots that divide ribbon knotted surfaces
Hans U. Boden, Ceyhun Elmacioglu, Anshul Guha +4
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a…
The Unbounded Denominators Conjecture
Frank Calegari, Vesselin Dimitrov, Yunqing Tang
We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). Our result includes also Mason's generalization o…
Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture
Davesh Maulik, Ananth N. Shankar, Yunqing Tang
Let be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve in characteristic . We prove that the geometric…
Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
Ananth N. Shankar, Arul Shankar, Yunqing Tang +1
Given a K3 surface over a number field with potentially good reduction everywhere, we prove that the set of primes of where the geometric Picard rank jumps is infinite.…
Reductions of abelian surfaces over global function fields
Davesh Maulik, Ananth N. Shankar, Yunqing Tang
Let be a non-isotrivial ordinary abelian surface over a global function field with good reduction everywhere. Suppose that does not have real multiplication by any real qua…
Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties
Wanlin Li, Elena Mantovan, Rachel Pries +1
We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo reduction of certain PEL-type Shimura varieties. We develop a clutching meth…
Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line
Wanlin Li, Elena Mantovan, Rachel Pries +1
By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Sh…
Newton polygons of cyclic covers of the projective line branched at three points
Wanlin Li, Elena Mantovan, Rachel Pries +1
We review the Shimura-Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective li…
Exceptional splitting of reductions of abelian surfaces
Ananth N. Shankar, Yunqing Tang
Heuristics based on the Sato--Tate conjecture suggest that an abelian surface defined over a number field has infinitely many places of split reduction. We prove this result for ab…
Effective bounds for Brauer groups of Kummer surfaces over number fields
Victoria Cantoral-Farfán, Yunqing Tang, Sho Tanimoto +1
We study effective bounds for Brauer groups of Kummer surfaces associated to the Jacobians of curves of genus defined over number fields.
Cycles in the de Rham cohomology of abelian varieties over number fields
Yunqing Tang
In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of -adic Tate…
Algebraic solutions of differential equations over the projective line minus three points
Yunqing Tang
The Grothendieck--Katz -curvature conjecture predicts that an arithmetic differential equation whose reduction modulo has vanishing -curvatures for {\em almost all} …