College of Arts and Sciences Endowed Professor

Algebraic geometry; commutative algebra; homological algebra; algebraic K-theory.

MS, Mathematics, 1978; PhD, Mathematics, 1982, University of Chicago

By appointment.

My research has been mainly in algebraic geometry, with an abiding interest in the study of algebraic cycles, particularly in the presence of singularities. I have established a number of results in this area, some obtained by making connections with Algebraic K-Theory.

I have wide research interests within algebraic geometry, ranging over classical algebraic geometry, algebraic cycles, algebraic groups, K-theory, commutative algebra, and Hodge theory, and like to work on problems lying in the overlaps between two or more of these fields, so that the perspectives of the different areas can be brought to bear simultaneously.

I have also worked also on cycles on nonsingular varieties; a technique using the diagonal cycle, originally considered by Bloch, was developed in (Math. Ann. (1983), American J. Math. (1983) into a workable tool for obtaining interesting results on algebraic cycles in many different situations, and has now been developed into a standard tool in the area.

In recent years, I have been working with Esnault, and other collaborators, on finiteness and boundedness statements related to the Étale Fundamental Groups of varieties in characterisitc *p* > 0.

Another thread in my work is on “oriented intersection theory” where classical intersection numbers are refined to invariants lying in Grothendieck-Witt groups. I had discussed local versions some years ago, and recently returned to this topic.

Other recent themes are on problems arising from cohomology and Hodge theory on singular varieties, where I have been collaborating with various colleagues on different questions. One such project revisits enriched Hodge structures that Bloch and I had introduced around 2000 to study K-theory in some new contexts. Another relates to studying a naturally defined subalgebra of the cohomology of a proper complex variety which supports a pure Hodge structure, compatible with the mixed structure on the whole cohomology.

- Srinivas, V., Algebraic K-theory, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008, xviii+341 pp. (reprint of Algebraic K- theory. Second Edition, Progress in Math., 90, Birkhäuser Boston, Inc., Boston, MA, 1996. xviii+341 pp.)
- Marc Levine; Simon Pepin Lehalleur; Vasudevan Srinivas; Euler characteristics of homogeneous and weighted homogeneous hypersurfaces, Advances in Math. 441 (2024), Article 109556, 86 pages.
- Lara, Marcin; Srinivas, Vasudevan; Stix, Jakob; Fundamental groups of proper varieties are finitely presented, C. R. Math. Acad. Sci. Paris 362 (2024), 51-54.
- Esnault, Helene; Srinivas, Vasudevan; Stix, Jakob; An obstruction to lifting to characteristic 0, Algebr. Geom. 10 (2023), no. 3, 327-347.
- Esnault, Helene; Shusterman, Mark; Srinivas, Vasudevan; Finite presenta- tion of the tame fundamental group, Selecta Math. (N.S.) 28 (2022), no. 2, Paper No. 37, 19 pp.
- Esnault, Helene; Srinivas, Vasudevan; Bounding ramification by covers and curves, Proc. Sympos. Pure Math., 104 American Mathematical Society, Providence, RI, 2021, 31-43.
- Esnault, Helene; Srinivas, Vasudevan; A relative version of Gieseker’s prob- lem on stratifications in characteristic
*p*> 0, Int. Math. Res. Not. IMRN(2019), no. 18, 5635-5648. - Esnault, Helene; Kindler, Lars; Srinivas, Vasudevan; A note on fierce rami- fication, J. Algebra 528 (2019), 250-259.
- Srinivas, Vasudevan; Takagi, Shunsuke; Nilpotence of Frobenius action and the Hodge filtration on local cohomology, Adv. Math. 305 (2017), 456-478.
- Rosenschon, Andreas; Srinivas, V.; Etale motivic cohomology and algebraic cycles, J. Inst. Math. Jussieu 15 (2016), no. 3, 511-537.
- Esnault, Helene; Srinivas, Vasudevan; Simply connected varieties in characteristic
*p*> 0, Compos. Math. 152 (2016), no. 2, 255-287.

(With an appendix by Bost, Jean-Benoıt, ‘Algebraization of formal mor- phisms and formal subbundles’). - Bloch, Spencer; Huang, An; Lian, Bong H.; Srinivas, Vasudevan; Yau, Shing- Tung; On the holonomic rank problem, J. Differential Geom. 97 (2014), no. 1, 11-35.
- Esnault, Hlne; Srinivas, Vasudevan; Algebraic versus topological entropy for surfaces over finite fields, Osaka J. Math. 50 (2013), no. 3, 827-846.
- Srinivas, Vasudevan; Algebraic cycles on singular varieties. Proceedings of the International Congress of Mathematicians, 2010. Invited lectures. Volume II, 603-623.