TY - JOUR
T1 - A heuristic for the distribution of point counts for random curves over a finite field
JF - Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences
JO - Philos Transact A Math Phys Eng Sci
M3 - 10.1098/rsta.2014.0310
VL - 373
IS - 2040
AU - Achter, Jeffrey D.
AU - Erman, Daniel
AU - Kedlaya, Kiran S.
AU - Wood, Melanie Matchett
AU - Zureick-Brown, David
Y1 - 2015/04/28
UR - http://rsta.royalsocietypublishing.org/content/373/2040/20140310.abstract
N2 - How many rational points are there on a random algebraic curve of large genus g over a given finite field ? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q+1+1/(q−1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g.
ER -