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SUMMARY:Alexei Skorobogatov (Imperial)
DTSTART;VALUE=DATE-TIME:20211203T100000Z
DTEND;VALUE=DATE-TIME:20211203T110000Z
DTSTAMP;VALUE=DATE-TIME:20240624T064153Z
UID:HannoverNTAGS/1
DESCRIPTION:Title: Enriques quotients of K3 surfaces and associated Brauer classes\
nby Alexei Skorobogatov (Imperial) as part of Hannover Number Theory and A
rithmetic Geometry Seminar\n\n\nAbstract\nThis is a joint work in progress
with Domenico Valloni. Let X be a complex K3 surface with an Enriques quo
tient S. It is known that the Brauer group of S has a unique non-zero elem
ent. Beauville gave a criterion for the natural map from Br(S) to Br(X) to
be injective. Extending a result of Keum\, who proved that every Kummer s
urface has an Enriques quotient\, we show for an arbitrary Kummer surface
X that every element of Br(X) of order 2 comes from an Enriques quotient o
f X. Work of Ohashi implies that in some `generic' cases this gives a bije
ction between the set of elements of order 2 in Br(X) and the set of Enriq
ues quotients of X.\n
LOCATION:https://researchseminars.org/talk/HannoverNTAGS/1/
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SUMMARY:Teppei Takamatsu (Kyoto University)
DTSTART;VALUE=DATE-TIME:20230414T084500Z
DTEND;VALUE=DATE-TIME:20230414T094500Z
DTSTAMP;VALUE=DATE-TIME:20240624T064153Z
UID:HannoverNTAGS/2
DESCRIPTION:Title: On Quasi-Frobenius-splitting\nby Teppei Takamatsu (Kyoto Univers
ity) as part of Hannover Number Theory and Arithmetic Geometry Seminar\n\n
\nAbstract\nIn algebraic geometry of positive characteristics\, singularit
ies defined by the Frobenius map\, including the notion of Frobenius-split
ting\, have played a crucial role.\nYobuko introduced the notion of quasi-
Frobenius-splitting and Frobenius-split heights\, which generalize and qua
ntify the notion of F-splitting\, and proved that Frobenius-split heights
coincide with Artin-Mazur heights for Calabi-Yau varieties.\nIn this talk\
, I want to explain recent results obtained on quasi-Frobenius-splitting (
specifically\, some criteria and properties).\nThis talk is based on joint
work with Tatsuro Kawakami\, Hiromu Tanaka\, Jakub Witaszek\, Fuetaro Yob
uko\, and Shou Yoshikawa.\n
LOCATION:https://researchseminars.org/talk/HannoverNTAGS/2/
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