Selmer Group Heuristics and Sieves
نویسنده
چکیده
In the past decade or so, the most elementary of the sieve methods of analytic number theory has been adapted to a geometric setting. In this geometric setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over Z. We will present the method and some of the results that have been proved using it. For instance, the probability that a plane curve over F2 is smooth is asymptotically 21/64 as the degree tends to infinity.
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