{"id":1457,"date":"2019-05-12T13:28:17","date_gmt":"2019-05-12T10:28:17","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1457"},"modified":"2019-05-23T22:57:48","modified_gmt":"2019-05-23T19:57:48","slug":"this-thursday-at-1200-u-haifa-topology-geometry-seminar-on-may-16-2019","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1457","title":{"rendered":"This Thursday at 12:00, U. Haifa Topology &#038; Geometry seminar on May 16, 2019"},"content":{"rendered":"<p style=\"font-weight: 400;\"><strong><u>Geometry\u00a0&amp; Topology Seminar<\/u><\/strong><\/p>\n<p style=\"font-weight: 400;\">\n<p style=\"font-weight: 400;\">Speaker:\u00a0\u00a0Uriya First\u00a0(University of Haifa)<\/p>\n<p style=\"font-weight: 400;\">Topic:\u00a0\u00a0\u00a0Azumaya algebras without involution<\/p>\n<p style=\"font-weight: 400;\">Place:\u00a0\u00a0\u00a0 room 614 in the Science &amp; Education Building<\/p>\n<p style=\"font-weight: 400;\">Time\u00a0 \u00a012:00<\/p>\n<p style=\"font-weight: 400;\">Date:\u00a0 Thursday, May 16, 2019<\/p>\n<p style=\"font-weight: 400;\">\n<p style=\"font-weight: 400;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<strong><u>Abstract<\/u><\/strong><strong><u>:<\/u><\/strong><\/p>\n<p>Let R\/S be a quadratic Galois extension of commutative rings with nontrivial automorphism s (definitions will be recalled during the talk). A locally free R-algebra is called Azumaya if the specialization of A to every geometric point of Spec R is a matrix algebra. Brauer equivalence classes of Azumaya algebras form the Brauer group, an important cohomological invariant of R.<\/p>\n<p>A theorem of Saltman characterizes the Brauer classes in Braur group of R admitting a representative with an s-involution, i.e., an involution whose restriction to the center R is s. Combined with a later proof of Knus, Parimala and Srinivas, it implies that if A is an Azumaya algebra that is Brauer equivalent to one admitting an s-involution, then it is Brauer equivalent to an algebra of degree 2*deg(A) admitting an s-involution.<\/p>\n<p>I will discuss a joint work with Ben Williams where we use C_2-equivariant homomotopy theory to show that 2*deg(A) cannot be improved in general, at least for certain values of deg(A).<\/p>\n<p>For comparison, when R is assumed to be semilocal, Saltman showed that A itself admits an involution, and so 2*deg(A) is not the lowest degree possible for a representative with an s-involution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometry\u00a0&amp; Topology Seminar Speaker:\u00a0\u00a0Uriya First\u00a0(University of Haifa) Topic:\u00a0\u00a0\u00a0Azumaya algebras without involution Place:\u00a0\u00a0\u00a0 room 614 in the Science &amp; Education Building Time\u00a0 \u00a012:00 Date:\u00a0 Thursday, May 16, 2019 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Abstract: Let R\/S be a quadratic Galois extension of commutative rings with nontrivial&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1457\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,4],"tags":[],"class_list":["post-1457","post","type-post","status-publish","format-standard","hentry","category-gt-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1457"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1457\/revisions"}],"predecessor-version":[{"id":1458,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1457\/revisions\/1458"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}