### Algebraic cycles on certain desingularized nodal hypersurfaces, Math. Ann. 270,
p. 17-27 (1985).

The first sentence on p. 19 seems a bit obscure. Here is a better argument

that the map jstar is injective when i=2m-1:

In the commutative diagram in the middle of page 18 take i=2m-1.

Then r is an isomorphism. Also c and hence b is injective. The

kernel of l has weight 2m-2. Since morphisms in the category of

mixed Hodge structures are strict with respect to the weight filtration

(or since passing to weight graded pieces is an exact functor by

Deligne Hodge II), the intersection of the image of b and the kernel of l

is zero. Thus jstar is injective.

### An integral analog of the Tate conjecture for one dimensional cycles on varieties over finite fields, Math. Ann. 311, 493-500 (1998)

Proof of Proposition 1.9: The surjectivity of the map i_*:H--> H^4(Y) is a

consequence of the Lefschetz hyperplane theorem. This should have been

stated explicitly in the paper, but somehow fell through the cracks.

Here are the details:

Dropping the subscripts the we have an exact sequence,

H^4_V(Y,Z_l(2)) -c-> H^4(Y,Z_l(2)) --> H^4(Y-V,Z_l(2)),

in which the final term is zero, since Y-V is a three dimensional affine

variety [Mi, VI.7.2], and the first term is isomorphic to H^2(V,Z_l(1))

and the map c may be identified with the Gysin map by [Mi, VI.5.4b],

where the references are to Milne's book on etale cohomology.

p. 499 line 7 the S_i in normal font should be in the script font.

### Albanese Standard and Albanese Exotic Varieties, J. London Math. Soc.
(2) 74 (2006) 304-320.

The proof of Lemma 7.8 should have explicitly mentioned that the map, $\dot {\rho }_*$,

in the diagram is an isomorphism. Indeed this is already true on the level of

fundamental groups by the proof of 7.7.

Numerous errors were introduced by the editor. Most were caught in the

course of correcting the proofs, but the following two slipped by:

p. 305 statement of Proposition 1.4: Replace "albanese" with "abelian".

p. 309 statement of Proposition 3.5: Delete "We say that".

### The Geometric Genus of a Desingularized Fiber Product of Elliptic Surfaces

Proof of Lemma 2.2: Given g in G let E^g denote $E\times _K\tilde K$

viewed as a $\tilde K$ scheme via composing the structure morphism with

$g:\tilde K\to \tilde K$. Then g:E^g-->$E\times _K\tilde K$ is defined

over $\tilde K$. Apply the universal mapping property of the Neron model

to this map.