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<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman','serif'"><STRONG><U>SEMINARI
DI MATEMATICA<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" /><o:p></o:p></U></STRONG></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left" align=left><SPAN
style="FONT-SIZE: 12pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"><o:p> </o:p></SPAN></H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">Giovedì 25
novembre 2010</SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></H2>
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style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">ore <SPAN
style="mso-no-proof: yes">16.00</SPAN><o:p></o:p></SPAN></P>
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style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><U><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
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style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Pisa<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">(Aula <SPAN
style="mso-no-proof: yes">Bianchi</SPAN>)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'">Clemens
Fuchs</SPAN></B><SPAN
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><I style="mso-bidi-font-style: normal"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'">Politecnico ETH
di Zurigo<B style="mso-bidi-font-weight: normal"><SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></B></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN lang=EN-US
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Terrà
un seminario dal titolo:<o:p></o:p></SPAN></P>
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style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><SPAN
lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 26pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">“On
effective versions of a theorem due to Shafarevich”<o:p></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><FONT
size=3>Abstract:<o:p></o:p></FONT></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><o:p><FONT
size=3> </FONT></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Let
K be a number field and let S be a finite set of places of K. A classical
theorem of Shafarevich says that there are only finitely many K-isomorphism
classes of elliptic curves over K with good reduction outside S. An effective
version of this statement for K=Q was already proved by Coates. In the talk we
discuss an extension to arbitrary number fields. We give explicit bounds and
compare them with the one obtained by Coates. One of the important features of
the result is that we view an elliptic curve as a purely geometric object which
is natural and gives flexibility for further generalisations. This is joint work
with R. von Känel and G. Wüstholz.<B style="mso-bidi-font-weight: normal"><SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></B></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><o:p> </o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><o:p> </o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><o:p> </o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 10pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US; mso-no-proof: yes"><o:p> </o:p></SPAN></I></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Tutti gli
interessati sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"><o:p> </o:p></SPAN></P>
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style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><FONT
face="Times New Roman"><SPAN style="mso-ansi-language: IT"><SPAN
style="mso-tab-count: 2"><FONT
size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT">Classe
di Scienze<o:p></o:p></SPAN></FONT></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P></FONT></DIV>
<DIV><FONT face=Arial
size=2>--------------------------------------------------------------------------------<BR>Valeria
Giuliani<BR>Scuola Normale Superiore<BR>Servizio Supporto Attività Didattiche -
Scienze<BR>Tel. 050-509260<BR>Fax. 050-509045<BR>Piazza dei Cavalieri,
7<BR>56126 Pisa<BR>E-Mail: <A
href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</A> <BR>E-Mail: <A
href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</A></FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Le informazioni contenute nella presente e-mail e
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diffusione, distribuzione e/o copiatura di tali informazioni da parte di
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questa e-mail per errore o senza esserne legittimato è invitato a darne
immediatamente notizia al mittente tramite fax o e-mail e a
distruggerla.<BR>Grazie.</FONT></DIV>
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