1,313 research outputs found
Brauer Groups and Tate-Shafarevich Groups
Let XK be a proper, smooth and geometrically connected curve over a global field K. In this paper we generalize a formula of Milne relating the order of the Tate-Shafarevich group of the Jacobian of XK to the order of the Brauer group of a proper regular model of XK. We thereby partially answer a question of Grothendieck
Algebraic cycles on Severi-Brauer schemes of prime degree over a curve
Let be a perfect field and let be a prime number different from the
characteristic of . Let be a smooth, projective and geometrically
integral -curve and let be a Severi-Brauer -scheme of relative
dimension . In this paper we show that contains
a subgroup isomorphic to for every in the range . We deduce that, if is a number field, then is finitely
generated for every in the indicated range.Comment: 6 page
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