Motivic invariants of birational maps

HY Lin, E Shinder - Annals of Mathematics, 2024 - projecteuclid.org
We construct invariants of birational maps with values in the Kontsevich--Tschinkel group
and in the truncated Grothendieck groups of varieties. These invariants are morphisms of …

[PDF][PDF] Cycle class maps and birational invariants

B Hassett, Y Tschinkel - arXiv preprint arXiv:1908.00406, 2019 - arxiv.org
arXiv:1908.00406v1 [math.AG] 1 Aug 2019 Page 1 arXiv:1908.00406v1 [math.AG] 1 Aug 2019
CYCLE CLASS MAPS AND BIRATIONAL INVARIANTS BRENDAN HASSETT AND YURI …

Curve classes on conic bundle threefolds and applications to rationality

S Frei, L Ji, S Sankar, B Viray, I Vogt - arXiv preprint arXiv:2207.07093, 2022 - arxiv.org
We undertake a study of conic bundle threefolds $\pi\colon X\to W $ over geometrically
rational surfaces whose associated discriminant covers $\tilde {\Delta}\to\Delta\subset W …

Arithmetic occult period maps

J Achter - arXiv preprint arXiv:1904.04288, 2019 - arxiv.org
Several natural complex configuration spaces admit surprising uniformizations as arithmetic
ball quotients, by identifying each parametrized object with the periods of some auxiliary …

Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties

C Vial - arXiv preprint arXiv:1803.00857, 2018 - arxiv.org
We prove Bloch's conjecture for correspondences on powers of complex abelian varieties,
that are" generically defined". As an application we establish vanishing results for (skew-) …

Derived equivalent threefolds, algebraic representatives, and the coniveau filtration

JD Achter, S Casalaina-Martin, C Vial - Mathematical Proceedings of …, 2019 - cambridge.org
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field
have isomorphic Chow motives. The conjecture is known for curves, and was recently …

[HTML][HTML] Motivic periods and Grothendieck arithmetic invariants

F Andreatta, L Barbieri-Viale, A Bertapelle… - Advances in …, 2020 - Elsevier
We construct a period regulator for motivic cohomology of an algebraic scheme over a
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …

Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons

JD Achter, S Casalaina-Martin, C Vial - Forum of Mathematics …, 2019 - cambridge.org
For families of smooth complex projective varieties, we show that normal functions arising
from algebraically trivial cycle classes are algebraic and defined over the field of definition of …

The Walker Abel–Jacobi map descends

JD Achter, S Casalaina-Martin, C Vial - Mathematische Zeitschrift, 2022 - Springer
For a complex projective manifold, Walker has defined a regular homomorphism lifting
Griffiths' Abel–Jacobi map on algebraically trivial cycle classes to a complex abelian variety …

Motivic periods and Grothendieck arithmetic invariants

A Fabrizio, L Barbieri-Viale, A Bertapelle… - ADVANCES IN …, 2020 - research.unipd.it
We construct a period regulator for motivic cohomology of an algebraic scheme over a
subfield of the complex numbers. For the field of algebraic numbers we formulate a period …