Errata: Fields of definition for some Hodge cycles

Math. Ann. 285 (1989), 289-295

• page 291: In (2.1), replace "relative dimension" by "relative dimension n".
• page 292, line 13 from bottom: insert "A =" at the beginning of the line.

Errata: Abelian varieties and the general Hodge conjecture

Compositio Math. 109 (1997), 341-355

• page 341, line 7 from bottom: replace V(-r) by V(r).
• page 345, line 4: replace (-r) by (r).
• Proposition 4.4.1 is false. Consequently,
  • Theorem 5.1 remains true (with minor modifications to the proof) provided that abelian varieties of type III are excluded.
  • Theorem 6.1 is false.

Errata: Filtrations on the cohomology of abelian varieties

CRM Proc. Lecture Notes 24 (2000), 3-12

• page 7, line 10: replace V(-r) by V(r).
• page 9, §7.1: item 2 is incorrect (see errata to next paper).
• page 10, line 20: replace U(-1) by U(1).

Errata: Hodge structures on abelian varieties of CM-type

J. Reine Angew. Math 534 (2001), 33-39

• Theorem 3.1 as stated is false. The error is essentially the same as in Proposition 4.4.1 of Abelian varieties and the general Hodge conjecture (see above). Consequently, some of the examples in Section 4 are incorrect. Correct results and examples may be found in Hodge structures of CM-type, J. Ramanujan Math. Soc. 20 (2005), 155-162..

Errata: Hodge structures on abelian varieties of type III

Ann. of Math. (2) 155 (2002), 915-928

• page 922: Add to the hypotheses of Theorem 4.1 that the center of D (the endomorphism algebra of A) is Q.

Last revision: September 23, 2011