69 citations · 200 across the 15 of their papers we have counts for
5 papers · 1 filter
Diophantine and tropical geometry, and uniformity of rational points on curves
Eric Katz, Joseph Rabinoff, David Zureick-Brown
We describe recent work connecting combinatorics and tropical/non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curve…
Uniform bounds for the number of rational points on curves of small Mordell--Weil rank
Eric Katz, Joseph Rabinoff, David Zureick-Brown
Let be a curve of genus over a number field of degree . The conjectural existence of a uniform bound on the number of -rational po…
The Theory of Witt Vectors
Joseph Rabinoff
This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (…
Optimal quotients of Jacobians with toric reduction and component groups
Mihran Papikian, Joseph Rabinoff
Let J be a Jacobian variety with toric reduction over a local field K. Let J -> E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the…
Higher-level canonical subgroups for p-divisible groups
Joseph Rabinoff
Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is s…