Zeta functions with p adic cohomology

David Roe

Description

Zeta functions with p-adic cohomology David Roe Harvard University / University of Calgary Geocrypt 2011 David Roe ( Harvard University / University of Calgary )Zeta functions with p-adic cohomology 1 / 28

• algebraic de rham complex over


• fq


• a?zq fq


• weil cohomology


• monsky-washnitzer cohomology


• fq-rational points

Sujets

• Harvard University
• Weil cohomology theory
• Monsky?Washnitzer cohomology

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 8
• Langue: English

Extrait

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David Roe

Geocrypt 2011

Zeta functions withp-adic cohomology

Harvard University / University of Calgary

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2

Hyperelliptic Curves

Beyond dimension 1

4

3

1

Timings

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Outline

Algorithm for hypersurfaces

y2/2

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p-adic point counting

82

for somef(x)∈F q [x]. Kedlaya’s key idea is that we can determine the size ofX(F q )from the action of Frobenius on a Weil cohomology theory applied toX.

Kedlaya [Ked01] gives an algorithm for computing the number of F q -rational points on a hyperelliptic curve using p-adic cohomology. Suppose thatXis a hyperelliptic curve of genusg, whose affine locus is defined by the equation y 2 =f(x)

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