Zeta functions with p adic cohomology
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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
Voir
- algebraic de rham complex over
- fq
- a?zq fq
- weil cohomology
- monsky-washnitzer cohomology
- fq-rational points
David Roe
Geocrypt 2011
Zeta functions withp-adic cohomology
Harvard University / University of Calgary
2
Hyperelliptic Curves
Beyond dimension 1
4
3
1
Timings
ologohom8
Outline
Algorithm for hypersurfaces
y2/2
p-adic point counting
82
for somef(x)∈Fq[x]. Kedlaya’s key idea is that we can determine the size ofX(Fq)from the action of Frobenius on a Weil cohomology theory applied toX.
Kedlaya [Ked01] gives an algorithm for computing the number of Fq-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 y2=f(x)
winsp-thicadhoco
