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# FUTUR. Portal de la Producció Científica dels Investigadors de la UPC

## Square-free discriminants of Frobenius rings

Autor
David, C.; Jimenez, J.
Tipus d'activitat
Article en revista
Revista
International journal of number theory
Data de publicació
2010-09
Volum
6
Número
6
Pàgina inicial
1391
Pàgina final
1412
DOI
https://doi.org/10.1142/S1793042110003599
Repositori
http://hdl.handle.net/2117/10419
URL
http://www.mathstat.concordia.ca/faculty/cdavid/PAPERS/SFdiscriminants-2008.pdf
Resum
Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated by the Frobenius element $\pi_p$. When the curve has complex multiplication (CM), this is always a fixed field as the prime varies. However, when the curve has no CM, very little is known, not only about the order, but about the fields that might appear as algebra of endomorphisms ...
Citació
David, C.; Jimenez, J. Square-free discriminants of Frobenius rings. "International journal of number theory", Setembre 2010, vol. 6, núm. 6, p. 1391-1412.
Grup de recerca
MAK - Matemàtica Aplicada a la Criptografia