4 papers
Isogenies of certain abelian varieties over finite fields with p-ranks zero
Steve Thakur
We study the isogenies of certain abelian varieties over finite fields with non-commutative endomorphism algebras with a view to potential use in isogeny-based cryptography. In par…
Abelian varieties with prescribed embedding and full embedding degrees
Steve Thakur
We study the problem of the embedding degree of an abelian variety over a finite field which is vital in pairing-based cryptography. In particular, we show that for a prescribed CM…
On some abelian varieties of type IV
Steve Thakur
We study a certain class of simple abelian varieties of type (in Albert's classification) over number fields with Mumford-Tate groups of type . In particular, we s…
Reductions of abelian varieties of generalized Mumford type
Steve Thakur
We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing -adic monodromy groups of t…