Alena Pirutka

Email: pirutka(a)cims(tochka)nyu(tochka)edu
Office: 611

Publications and preprints

• Cohomologie non ramifiée en degré trois d'une variété de Severi-Brauer, C. R. Acad. Sci. Paris, Ser. I 349 (2011), 369-373 (version on arXiv).
• Sur le groupe de Chow de codimension deux des variétés sur les corps finis, Algebra and Number Theory 5-6 (2011), 803-817.
• R-equivalence on low degree complete intersections, J. Algebraic Geom. 21 (2012), 707-719.
• R-équivalence sur les familles de variétés rationnelles et méthode de la descente, Journal de Théorie des Nombres de Bordeaux 24, no. 2, (2012), 461-473.
• Invariants birationnels dans la suite spectrale de Bloch-Ogus, Journal of K-theory 10 (2012), 565-582.
• A bound to kill the ramification over function fields, J. Algebra 377 (2013), 173-178 .
• (with F. Charles) La conjecture de Tate entière pour les cubiques de dimension quatre sur un corps fini, Compositio Mathematica 151, no. 2, (2015), 253-264.
• (with N. Yagita) Note on the counterexamples for the integral Tate conjecture over finite fields, Documenta Math. Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday, (2015), 501-511.
• Sur la cohomologie non ramifiée en degré trois d'un produit, Bulletin de la SMF 144, no. 1, (2016), 53-75.
• On a local-global principle for H3 of function fields of surfaces over a finite field, In: A. Auel, B. Hassett, A. Várilly-Alvarado, B. Viray, Brauer Groups and Obstruction Problems. Progress in Mathematics 320, Birkhäuser Basel, 2017.
• (with J.-L. Colliot-Thélène) Hypersurfaces quartiques de dimension 3 : non rationalité stable, Ann. Sci. Ecole Norm. Sup. (2) 49 (2016) 371-397.
• (with J.-L. Colliot-Thélène) Revêtements cycliques qui ne sont pas stablement rationnels, Izvestiya RAN, Ser. Mat. 80, no. 4, (2016), 35-47.
• (with F. Bogomolov and A. Silberstein) Families of disjoint divisors on varieties, European Journal of Mathematics, 2016, Volume 2, Issue 4, 917-928.
• Varieties that are not stably rational, zero-cycles and unramified cohomology, in Algebraic Geometry (Salt Lake City, UT, 2015), Proc. Sympos. Pure Math., 97, 459-484. Amer. Math. Soc., Providence, RI, 2018.
• (with B. Hassett and Y. Tschinkel) Stable rationality of quadric surface bundles over surfaces, Acta Mathematica, 220, 341-365, (2018) .
• (with B. Hassett and Y. Tschinkel) A very general quartic double fourfold is not stably rational, Algebraic Geometry, 6(1), 64-75, (2019) .
• (with B. Hassett and Y. Tschinkel) Intersections of three quadrics in P⁷, Surveys in Differential Geometry, 22(1), 259-274, (2017).
• (with A. Auel and C. Böhning) Stable rationality of quadric and cubic surface bundle fourfolds, European Journal of Mathematics (2018), 1-29.
• (with J.-L. Colliot-Thélène) Troisième groupe de cohomologie non ramifiée d'un solide cubique sur un corps de fonctions d'une variable, Epijournal de géométrie algébrique (EPIGA) volume 2, article no.13 (2018).
• (with A. Auel, C. Böhning and H.-C. Graf v. Bothmer) Conic bundles with nontrivial unramified Brauer group over threefolds, Journal of Algebraic Geometry 29 (2020), no.2, 285-327.
• (with A. Cadoret) Reconstructing function fields from Milnor K-theory, Algebra and Number Theory 15 (2021), no.9, 2261-2288.
• (with F. Bogomolov and C. Böhning ) On stable cohomology of central extensions of elementary abelian groups, In: Ahmadinezhad, H. and Kasprzyk, A. and Mori, S., (eds.) London Mathematical Society. Lecture Note Series. Cambridge University Press (2021).
• (with D. Harbater and D. Krashen) Local-global principles for curves over semi-global fields, Bull. Lond. Math. Soc. 53 (2021), no. 1, 177-193.
• (with F. Charles) Finitude uniforme pour les cycles de codimension 2 sur les corps de nombres (2022), to appear in Perspectives on four decades of Algebraic Geometry: in Memory of Alberto Collino, Progress in Mathematics.
• Cubic surface bundles and the Brauer group, preprint (2023).
• (with J.-L. Colliot-Thélène) Certaines fibrations en surfaces quadriques réelles, preprint (2024).
• (with Zh. Zhang) Computing the equivariant Brauer group, preprint (2024).
• (with A. Cadoret) Uniform bounds for obstructions to the integral Tate conjecture, preprint (2024).

Some talks and courses

• Mini-course 'Diagonal Arithmetics' (program 'Rational points', l'IMPA, Rio de Janeiro 25-29 May 2015): slides, exercises.
• Slides for the talk Algebraic cycles on varieties over finite fields, CIRM, conference Arithmétique, Géométrie, Cryptographie et Théorie des Codes, May 2015.
• Notes for my talk for the working group on cohomological invariants, May 2015: notes, slides.
• Talk at kafemath, February 12, 2015.
• Notes for the summer school in Yaroslavl, July 2012.
• Notes for my talk at the summer school in Grenoble Moduli spaces of stable curves and R-equivalence.

Conferences, theses, and other notes

• Conference on Algebraic Geometry and Number Theory on the occasion of Jean-Louis Colliot-Thélène's 70th birthday, Florence, December, 4-December, 6, 2017.
• Conference: Arithmetic Algebraic Geometry, Courant Institute, August, 29 - September, 2, 2016.
• Habilitation.
• My thesis Deux contributions à l'arithmétique des variétés : R-équivalence et cohomologie non ramifiée.
• Magister thesis.
• Master thesis.