TY - JOUR
T1 - Tate Duality in Positive Dimension over Function Fields
AU - Rosengarten, Zev
N1 - Publisher Copyright:
© 2023 American Mathematical Society.
PY - 2023/10
Y1 - 2023/10
N2 - We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on the recent work of Česnavičius ("Poitou-Tate without restrictions on the order,"2015) extending these results to all finite commutative group schemes. We concentrate mainly on the more difficult function field setting, giving some remarks about the number field case along the way.
AB - We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all affine commutative group schemes of finite type, building on the recent work of Česnavičius ("Poitou-Tate without restrictions on the order,"2015) extending these results to all finite commutative group schemes. We concentrate mainly on the more difficult function field setting, giving some remarks about the number field case along the way.
UR - http://www.scopus.com/inward/record.url?scp=85166959301&partnerID=8YFLogxK
U2 - 10.1090/memo/1444
DO - 10.1090/memo/1444
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AN - SCOPUS:85166959301
SN - 0065-9266
VL - 290
SP - 1
EP - 217
JO - Memoirs of the American Mathematical Society
JF - Memoirs of the American Mathematical Society
IS - 1444
ER -