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7 papers · 1 filter
Local monodromy of p-adic differential equations: an overview
Kiran S. Kedlaya
This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often…
Quantum computation of zeta functions of curves
Kiran S. Kedlaya
We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorith…
In search of Robbins stability
Kiran S. Kedlaya, James G. Propp
We speculate on whether a certain p-adic stability phenomenon, observed by David Robbins empirically for Dodgson condensation, appears in other nonlinear recurrence relations that…
Integral points on elliptic curves and 3-torsion in class groups
H. A. Helfgott, A. Venkatesh
We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and metho…
Computing zeta functions via p-adic cohomology
Kiran S. Kedlaya
We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some…
Frobenius modules and de Jong's theorem
Kiran S. Kedlaya
Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W…