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Matt Broe
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Matt Broe
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Preprints

  • The Beilinson-Bloch conjecture for some cubic threefolds over global function fields. arXiv link.  . 

  • On the Beilinson-Bloch conjecture over function fields. arXiv link.

Talk Notes

These are notes for expository talks I have given. 

  • Algebraic cycles and values of L-functions, BU Math 842, spring 2025. Notes.

  • Basics of higher category theory, BU topology and number theory learning seminar, spring 2025. Notes.


Errata

Click here for a list of some errors in the current versions of my preprints which I am aware of (so far I have not found any which significantly affect the results). They will be fixed in future versions.

The Beilinson-Bloch conjecture for some cubic threefolds over global function fields:

  1. After proposition 2.1, it should say "motives of products of geometrically integral curves are of abelian type." 

  2. Definition 2.2 should be stated for smooth projective schemes (or even arbitrary motives), rather than just varieties.

  3. In the proof of corollary 3.4(ii), the definition of "variety" in the referenced paper of Vial does not require a variety to be an irreducible scheme. In the notation/terminology of the proof, C should thus actually be a disjoint union of curves, and S a disjoint union of varieties of dimension at most 2. Also, the argument only shows (and only needs) that the cohomology of X is 1-semisimple in the sense of conjecture 3.2(ii) (the current version says "its cohomology is semisimple", which is a stronger claim).

  4. In the last paragraph of the proof of lemma 4.1, it should say "Such a product has motive of abelian type, and any model of it over a finite field satisfies the Tate conjecture for divisors".

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