Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

Rains, Eric; Rubin, Karl; Scholl, Travis; Sharif, Shahed; Silverberg, Alice

doi:10.2140/ant.2021.15.711

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Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

Eric Rains, Karl Rubin, Travis Scholl, Shahed Sharif and Alice Silverberg

Vol. 15 (2021), No. 3, 711–727

DOI: 10.2140/ant.2021.15.711

Abstract

We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results shed light on a question raised by Boneh et al. (J. Math. Cryptol. 14:1 (2020), 5–14) concerning a proposal for multiparty noninteractive key exchange.

Keywords

abelian varieties, polarizations

Mathematical Subject Classification 2010

Primary: 14K10

Secondary: 11G10, 11G15

Milestones

Received: 16 December 2019

Revised: 10 July 2020

Accepted: 17 October 2020

Published: 20 May 2021

Authors

Eric Rains
Department of Mathematics California Institute of Technology Pasadena, CA United States

Karl Rubin
Department of Mathematics University of California Irvine, CA United States

Travis Scholl
Department of Mathematics University of California Irvine, CA United States

Shahed Sharif
Department of Mathematics California State University San Marcos San Marcos, CA United States

Alice Silverberg
Department of Mathematics University of California Irvine, CA United States

Vol. 15, No. 3, 2021