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タイトル	Is there a Birch and Swinnerton-Dyer conjecture for Dedekind Zeta functions?
開催日時	2026年2月25日（水）16:30 - 17:30
主催者
講演者	Christopher Deninger 氏 (University of Münster)
場所	慶應義塾大学理工学部（矢上キャンパス）14棟631A
内容	By the BSD conjecture the order of vanishing at s=1 of the L-function of an elliptic curve E over Q should be the rank of E(Q). Correspondingly, one may ask for a vector space V(K) for every number field K whose dimension is the order of vanishing of the Dedekind zeta function of K at s=1/2. We do not know a good candidate for V(K). However cohomological considerations suggest that V(K) should have several extra structures and be functorial in K. Assuming an unpublished conjecture of Serre we prove that such an enhanced functor V exists and is unique up to isomorphism. It’s automorphism group is an abelian 2-group.
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