99 citations · 492 across the 111 of their papers we have counts for
8 papers · 1 filter
Rigid local systems and alternating groups
Robert M. Guralnick, Nicholas M. Katz, Pham Huu Tiep
In earlier work, Katz exhibited some very simple one parameter families of exponential sums which gave rigid local systems on the affine line in characteristic p whose geometric (a…
Endomorphism fields of abelian varieties
Robert Guralnick, Kiran S. Kedlaya
We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrar…
Rigidity for F_4(p)
Frank Lübeck, Robert Guralnick, Jun Yu
We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and s…
Adequate subgroups
Robert Guralnick, Florian Herzig, Richard Taylor +1
We study adequate subgroups of over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a su…
The Automorphism Groups of a Family of Maximal Curves
Robert Guralnick, Beth Malmskog, Rachel Pries
The Hasse Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giuliet…
A new family of exceptional polynomials in characteristic two
Robert M. Guralnick, Joel E. Rosenberg, Michael E. Zieve
We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] bes…
Exceptional covers and bijections on rational points
Robert M. Guralnick, Thomas J. Tucker, Michael E. Zieve
We show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degre…
Polynomials which are locally reducible
R. Guralnick, M. Schacher, J. Sonn
Let be a global field and an integer. We show is composite if and only if there is an irreducible polynomial of degree which is reducible -ad…