49 citations · 86 across the 14 of their papers we have counts for
17 papers
Canonical lifts and -structures
James Borger, Lance Gurney
We extend the Serre-Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a -adic formal…
Explicit class field theory and the algebraic geometry of -rings
James Borger, Bart de Smit
We consider generalized -structures on algebras and schemes over the ring of integers of a number field . When , these agree with the -ring st…
Isocrystals associated to arithmetic jet spaces of abelian schemes
James Borger, Arnab Saha
Using Buium's theory of arithmetic differential characters, we construct a filtered -isocrystal associated to an abelian scheme over a -adically complete d…
On Frobenius and Fibers of Arithmetic Jet Spaces
James Borger, Arnab Saha
In this article, given a scheme we show the existence of canonical lifts of Frobenius maps in an inverse system of schemes obtained from the fiber product of the canonical prol…
Differential Characters of Drinfeld Modules and de Rham Cohomology
James Borger, Arnab Saha
We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differentia…
Canonical lifts of families of elliptic curves
James Borger, Lance Gurney
We show that the canonical-lift construction for ordinary elliptic curves over perfect fields of characteristic extends uniquely to arbitrary families of ordinary elliptic cu…