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## Fast Polynomial Factorization and Modular Composition

- K. Kedlaya, C. Umans
- Computer Science, MathematicsSIAM J. Comput.
- 1 November 2011

TLDR

## Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

- K. Kedlaya
- Mathematics
- 3 May 2001

We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the… Expand

## Relative P-adic Hodge Theory: Foundations

- K. Kedlaya, Ruochuan Liu
- Mathematics
- 4 January 2013

We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give… Expand

## A p-adic local monodromy theorem

- K. Kedlaya
- Mathematics
- 11 October 2001

We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential… Expand

## Fast Modular Composition in any Characteristic

- K. Kedlaya, C. Umans
- Computer Science49th Annual IEEE Symposium on Foundations of…
- 25 October 2008

TLDR

## p-adic Differential Equations

- K. Kedlaya
- Mathematics
- 26 July 2010

Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory… Expand

## Sato–Tate distributions and Galois endomorphism modules in genus 2

- Francesc Fit'e, K. Kedlaya, V. Rotger, Andrew V. Sutherland
- MathematicsCompositio Mathematica
- 30 October 2011

Abstract For an abelian surface A over a number field k, we study the limiting distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to… Expand

## Fourier transforms and $p$-adic ‘Weil II’

- K. Kedlaya
- MathematicsCompositio Mathematica
- 10 October 2002

We give a purity theorem in the manner of Deligne's ‘Weil II’ theorem for rigid cohomology with coefficients in an overconvergent $F$-isocrystal; the proof mostly follows Laumon's Fourier-theoretic… Expand

## The algebraic closure of the power series field in positive characteristic

- K. Kedlaya
- Mathematics
- 23 October 1998

For K an algebraically closed field, let K((t)) denote the quotient field of the power series ring over K. The “Newton-Puiseux theorem” states that if K has characteristic 0, the algebraic closure of… Expand

## Slope filtrations revisited.

- K. Kedlaya
- Mathematics
- 1 April 2005

We give a "second generation" exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these… Expand

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