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SUMMARY:Higher arithmetic Chow groups. - Souvik Goswami (Texas A&amp\;M Un
 iversity )
DTSTART:20200309T150000Z
DTEND:20200309T160000Z
UID:TALK140824@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>We give a new definition of higher arithmetic Chow group
 s for smooth projective varieties defined over a number field\, which is s
 imilar to Gillet and Soul&eacute\;&#39\;s definition of arithmetic Chow gr
 oups. We also give a compact description of the intersection theory of suc
 h groups. A consequence of this theory is the definition of a height pairi
 ng between two higher algebraic cycles\, of complementary dimensions\, who
 se real regulator class is zero. This description agrees with Beilinson&#3
 9\;s height pairing for the classical arithmetic Chow groups. We also give
  examples of the higher arithmetic intersection pairing in dimension zero 
 that is given by the Bloch-Wigner dilogarithm functions. This is based on 
 the joint work with Jos&eacute\; Burgos Gil (<a target="_blank" rel="nofol
 low" href="https://doi.org/10.1016/j.aim.2019.02.003">https://doi.org/10.1
 016/j.aim.2019.02.003</a>).</span>  <br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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