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 study geometric monodromy groups $ G_ {\geo,\sF_q} $ of the local systems $\sF_q $ on
the affine line over $\F_2 $ of rank $ D=\sqrt {q}(q-1) $, $ q= 2^{2n+ 1} $, constructed in\cite …

We develop the general theory of Airy sheaves of Laurent type, the local systems whose
trace functions have a particular “Airy-Laurent” shape. The main goal is to provide tools for …

Abstract Condition (S+), introduced in [17], plays a key role in the study of Kloosterman and
hypergeometric l-adic local systems in positive characteristic p. Prior results of [17],[20] …

We determine precisely which irreducible hypergeometric sheaves have an extraspecial
normalizer in characteristic 2 as their geometric monodromy groups. This resolves the last …

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite,
almost quasisimple and has the projective special linear group PSL n (q) with n≥ 3 as a …

We find all irreducible hypergeometric sheaves whose geometric monodromy group is finite,
almost quasisimple and has the projective special linear group $ PSL_n (q) $ with $ n\geq …

We study the arithmetic Fourier transforms of trace functions on general connected
commutative algebraic groups. To do so, we first prove a generic vanishing theorem for …

Abhyankar's conjecture, proved by Raynaud, Harbater and Pop, characterizes the finite
quotient groups of the étale fundamental group of affine algebraic groups over algebraically …