<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;" class=""><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Ilgilenen herkesi bekleriz.</div><div class=""><br class=""></div><div class="">Ergun Yalcin</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div class="" style="font-family: LiSungLight;">——————————</div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;">BILKENT ALGEBRA-TOPOLOGY SEMINAR</div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;">Speaker: Cihan Okay (University of Western Ontario, Canada)</div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;">Time: Aug 13, Thursday, 13:30-14:30</div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;">Place: Bilkent Math Department Seminar Room</div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;"><p class="" style="margin: 0in; font-family: Calibri;">Title: Towards a refinement of the Bloch-Kato conjecture</p><p class="" style="margin: 0in; font-family: Calibri;"><br class=""></p><p class="" style="margin: 0in; font-family: Calibri;">Abstract: The Bloch-Kato conjecture is the statement that the Galois cohomology of the </p><p class="" style="margin: 0in; font-family: Calibri;">absolute Galois group of a field which contains a primitive pth root of unity in mod p </p><p class="" style="margin: 0in; font-family: Calibri;">coefficients is isomorphic to Milnor K-theory reduced modulo p. This statement is now </p><p class="" style="margin: 0in; font-family: Calibri;">a theorem proved by Rost and Voevodsky. In other words it says that the cohomology </p><p class="" style="margin: 0in; font-family: Calibri;">ring of the absolute Galois group is generated by one dimensional classes. It is a natural </p><p class="" style="margin: 0in; font-family: Calibri;">question to find intermediate Galois extensions of the base field where every element </p><p class="" style="margin: 0in; font-family: Calibri;">in the cohomology ring decomposes into a sum of products of one dimensional classes. </p><p class="" style="margin: 0in; font-family: Calibri;">In degree two we answer this question by providing a tower of Galois extensions where indecomposable elements decompose in the next level of the tower. We also illustrate </p><p class="" style="margin: 0in; font-family: Calibri;">this refinement by directly computing the cohomology rings of superpythagorean fields </p><p class="" style="margin: 0in; font-family: Calibri;">and p-rigid fields. This is a joint work with J. Minac and S. Chebolu.</p><div class=""><br class=""></div></div><div class="" style="font-family: LiSungLight;">————————————————</div></div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;"><br class=""></div><div class="" style="font-family: LiSungLight;"><br class=""></div></body></html>