<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>早稲田大学高等研究所の秋吉と申します．</div><div><br></div><div>以下の要領で，高等研究所セミナー「可換環論における逆数学」を開催いたします．</div><div><br></div><div><span style="font-family: 'ＭＳ 明朝', serif;">ご都合よろしければぜひご参加ください。</span></div><div><span style="font-family: 'ＭＳ 明朝', serif;"><br></span></div><div><br></div>————————————————————————————————————————————————————————————<div><br></div><div>
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mso-font-kerning:0pt">次のようなセミナーを予定しております．参加自由です．</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-size: 14pt;">------------------------------------------------------------------------------</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"ＭＳ 明朝";
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mso-font-kerning:0pt">高等研究所主催セミナー</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"ＭＳ 明朝";
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mso-font-kerning:0pt">講演者：佐藤隆（東北大学理学研究科）</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"ＭＳ 明朝";
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mso-font-kerning:0pt">日時：</span><span lang="EN-US">6</span><span style="font-family:"ＭＳ 明朝";mso-ascii-font-family:Helvetica;mso-fareast-font-family:
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mso-font-kerning:0pt">場所：早稲田大学早稲田キャンパス</span><span lang="EN-US">9</span><span style="font-family:"ＭＳ 明朝";mso-ascii-font-family:Helvetica;mso-fareast-font-family:
"ＭＳ 明朝";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Helvetica;
mso-bidi-font-family:Helvetica;mso-font-kerning:0pt">号館</span><span lang="EN-US">5</span><span style="font-family:"ＭＳ 明朝";mso-ascii-font-family:Helvetica;
mso-fareast-font-family:"ＭＳ 明朝";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Helvetica;mso-bidi-font-family:Helvetica;mso-font-kerning:
0pt">階 第</span><span lang="EN-US">2</span><span style="font-family:"ＭＳ 明朝";
mso-ascii-font-family:Helvetica;mso-fareast-font-family:"ＭＳ 明朝";mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Helvetica;mso-bidi-font-family:Helvetica;
mso-font-kerning:0pt">会議室</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal"><span lang="EN-US">(URL: <a href="http://www.waseda.jp/wias/">http://www.waseda.jp/wias/</a>)<o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"ＭＳ 明朝";
mso-ascii-font-family:Helvetica;mso-fareast-font-family:"ＭＳ 明朝";mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Helvetica;mso-bidi-font-family:Helvetica;
mso-font-kerning:0pt">タイトル：可換環論における逆数学</span><span lang="EN-US"><o:p></o:p></span></p><p class="MsoNormal" align="left"><span lang="EN-US"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";mso-font-kerning:
0pt">アブストラクト：<span lang="EN-US"><o:p></o:p></span></span></p><p class="MsoNormal" align="left"><span lang="EN-US" style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";
mso-font-kerning:0pt"> </span></p><p class="MsoNormal" align="left"><span style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";mso-font-kerning:
0pt"> 本研究は「逆数学」の手法を用いて，数学史の観点も加味しながら，可換環論をメタ分析する，</span><span style="font-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-font-kerning:
0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";
mso-font-kerning:0pt">というものです．可換環論の歴史を大雑把に辿れば，十九世紀中盤の代数的整数論が動機となり，イデアル論を経て，二十世紀前半の抽象代数学の勃興という道筋が見えてきます．この抽象化にあたって，</span><span lang="EN-US" style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt">D. Hilbert, Van der Waerden, E. Noether</span><span style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";mso-font-kerning:
0pt">らの貢献が指摘できます．その一連の抽象化の中で，本質的に必要とされる公理はどのように変わっていったのでしょうか？ これまでに得られた結果から，可算な一般の可換環のクラスについて，その理論を展開するには，</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:
"MS Mincho";mso-font-kerning:0pt">算術的集合存在公理（体系</span><span lang="EN-US" style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt">ACA</span><span style="font-family:"MS Mincho";
mso-bidi-font-family:"MS Mincho";mso-font-kerning:0pt">）が必要かつ十分であることが示唆されます．一方，より狭いアルティン環のクラスの理論については，より弱い公理である弱ケーニッヒの補題（体系</span><span lang="EN-US" style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt">WKL</span><span style="font-family:"MS Mincho";
mso-bidi-font-family:"MS Mincho";mso-font-kerning:0pt">）が必要</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:
"MS Mincho";mso-font-kerning:0pt">かつ十分であることが</span><span lang="EN-US" style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt">C. Conidis</span><span style="font-family:"MS Mincho";
mso-bidi-font-family:"MS Mincho";mso-font-kerning:0pt">により示されています．それでは，整数環の素イデアル分解，ネータ環の準素イデアル分</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:
"MS Mincho";mso-font-kerning:0pt">解，</span><span lang="EN-US" style="font-family:
"Times New Roman";mso-fareast-font-family:"Times New Roman";mso-font-kerning:
0pt">PID</span><span style="font-family:"MS Mincho";mso-bidi-font-family:"MS Mincho";
mso-font-kerning:0pt">の単因子論など，各クラスの理論を特徴付ける公理はどのようなものになるのでしょうか？</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:
"MS Mincho";mso-font-kerning:0pt">本講演では，以上の結果を紹介するとともに，これからの研究を進めるにあたっての困難な点や，</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> </span><span style="font-family:"MS Mincho";mso-bidi-font-family:
"MS Mincho";mso-font-kerning:0pt">解決のアイディアについてお話しします．</span><span style="font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
mso-font-kerning:0pt"> <span lang="EN-US"><o:p></o:p></span></span></p><p class="MsoNormal"><span lang="EN-US"> </span></p><p class="MsoNormal"><span style="font-family:"ＭＳ 明朝";mso-ascii-font-family:Helvetica;
mso-fareast-font-family:"ＭＳ 明朝";mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Helvetica;mso-bidi-font-family:Helvetica;mso-font-kerning:
0pt">問い合わせ先：早稲田大学高等研究所 秋吉亮太</span><span lang="EN-US"> (<a href="mailto:georg.logic@aoni.waseda.jp">georg.logic@aoni.waseda.jp</a>)</span><span lang="EN-US"><o:p></o:p></span></p>
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