The study of exponential sums over finite fields goes back to Gauss. The importance of
estimating them goes back at least to Kloosterman's 1926 paper [Kl]. In the one-variable …

We study the possible structures of monodromy groups of Kloosterman and hypergeometric
sheaves on G _m G m in characteristic p. We show that most such sheaves satisfy a certain …

We continue the program set up in [KT5] to study the monodromy groups of hypergeometric
and Kloosterman sheaves. We gave there easy to apply criteria on these sheaves that their …

We construct explicit local systems on the affine line in characteristic p> 2, whose geometric
monodromy groups are the finite symplectic groups Sp 2 n (q) for all n⩾ 2, and others whose …

We first develop some basic facts about hypergeometric sheaves on the multiplicative group
$\mathbb {G} _m $ in characteristic $ p> 0$. Specializing to some special classes of …

We use hypergeometric sheaves on G _m/F _q G m/F q, which are particular sorts of rigid
local systems, to construct explicit local systems whose arithmetic and geometric …

We first develop some basic facts about hypergeometric sheaves on the multiplicative group
𝔾 m in characteristic p> 0. Certain of their Kummer pullbacks extend to irreducible local …

For powers q of any odd prime p and any integer n≥ 2, we exhibit explicit local systems, on
the affine line A 1 in characteristic p> 0 if 2| n and on the affine plane A 2 if 2∤ n, whose …

We construct hypergeometric sheaves whose geometric monodromy groups are the finite
symplectic groups Sp2n (q) for any odd n≥ 3, for q any power of an odd prime p. We …

A certain" condition (S)" on reductive algebraic groups was introduced in [GT2], in which a
slightly stronger condition (S+) was shown to have very strong consequences. We show that …