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Publications Influence

Fast Polynomial Factorization and Modular Composition

- Kiran S. Kedlaya, Christopher Umans
- Mathematics, Computer Science
- SIAM J. Comput.
- 1 November 2011

We obtain randomized algorithms for factoring degree $n$
univariate polynomials over $F_q$ requiring $O(n^{1.5 +
o(1)} log^{1+o(1)} q+ n^{1 + o(1)}log^{2+o(1)} q)$ bit operations.
When $log q <… Expand

154 22- PDF

Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

- Kiran S. 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

229 20- PDF

Relative P-adic Hodge Theory: Foundations

- Kiran S. Kedlaya, R. 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

134 16- PDF

A p-adic local monodromy theorem

- Kiran S. 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

162 13- PDF

Fast Modular Composition in any Characteristic

- Kiran S. Kedlaya, Christopher Umans
- Mathematics, Computer Science
- 49th Annual IEEE Symposium on Foundations of…
- 25 October 2008

TLDR

63 10- PDF

p-adic Differential Equations

- Kiran S. Kedlaya
- Mathematics
- 26 July 2010

Preface Introductory remarks Part I. Tools of p-adic Analysis: 1. Norms on algebraic structures 2. Newton polygons 3. Ramification theory 4. Matrix analysis Part II. Differential Algebra: 5.… Expand

118 7

The algebraic closure of the power series field in positive characteristic

- Kiran S. 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

84 6- PDF

Slope filtrations revisited.

- Kiran S. 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

89 5- PDF

Slope filtrations for relative Frobenius

- Kiran S. Kedlaya
- Mathematics
- 10 September 2006

The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring… Expand

57 5- PDF

Solving constrained Pell equations

- Kiran S. Kedlaya
- Computer Science, Mathematics
- Math. Comput.
- 1 April 1998

TLDR

50 5- PDF

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