Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Frobenius calculations of Picard groups and the Birch-Tate-Swinnerton-Dyer conjecture
HTML articles powered by AMS MathViewer

by Raymond T. Hoobler PDF
Trans. Amer. Math. Soc. 222 (1976), 345-352 Request permission


Let $Y \subset {{\text {P}}^m}$ be a subvariety of codimension d defined by an ideal I in char $p > 0$ with ${H^1}(Y,\mathcal {O}( - 1)) = 0$. If t is an integer greater than ${\log _p}(d)$ and ${H^i}(Y,{I^n}/{I^{n + 1}}) = 0$ for $n > > 0$ and $i = 1,2$, then ${\text {Pic}}(Y)$ is an extension of a finite p-primary group of exponent at most ${p^t}$ by $Z[\mathcal {O}(1)]$ and ${\text {Br}}’(Y)(p)$ is a group of exponent at most ${p^t}$. If Y is also smooth and defined over a finite field with $\dim Y < p$ and $p \ne 2$, then the B-T-SD conjecture holds for cycles of codimension 1. These results are proved by studying the etale cohomology of the Frobenius neighborhoods of Y in ${{\text {P}}^m}$.
  • Spencer Bloch, Algebraic $K$-theory and crystalline cohomology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 187–268 (1978). MR 488288
  • Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977, DOI 10.1007/BFb0067839
  • Raymond T. Hoobler, Cohomology of purely inseparable Galois coverings, J. Reine Angew. Math. 266 (1974), 183–199. MR 364258, DOI 10.1515/crll.1974.266.183
  • John T. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 93–110. MR 0225778
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 14C20, 14G20
  • Retrieve articles in all journals with MSC: 14C20, 14G20
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 345-352
  • MSC: Primary 14C20; Secondary 14G20
  • DOI:
  • MathSciNet review: 0437529