## [Distinguished Lecture]The Bloch-Beilinson Conjecture

Time: 2015-11-22
Published By:

**Speaker(s): ** Vasudevan Srinivas （school of mathematics, tifr）

**Time: ** 00:00-00:00 November 22, 2015

**Venue: ** 77201

Speaker: Vasudevan Srinivas （school of mathematics, tifr）

Place: 77201

Time: Nov. 22 3:30pm-4:30pm

The Bloch-Beilinson Conjectures are some of the deepest open questions in mathematics today, relating aspects of algebraic geometry, algebraic K-theory and number theory.

The conjectures have roots, on the one hand, in classical results (Euler, Riemann, Dedekind, Hilbert, Artin, etc.) on special values and zeroes of zeta functions, in the period upto the early 20th century.

Another source, somewhat more recent (going upto the mid 1970's) is work of Tate, Iwasawa, Lichtenbaum, Quillen and Borel, which brought in the role of algebraic K-theory.

The most recent inspiration, beginning with several key calculations of Bloch, relate these to algebraic geometry. Bloch's vision was articulated in a general, more precise form by Beilinson, around 1982, resulting in what we now call the Bloch-Beilinson Conjectures. There are also refinements (e.g. the Bloch-Kato conjectures).

In fact there is tantalising, but rather meagre, evidence to support these conjectures, inspite of some 30 years of effort by mathematicians.

My lecture will attempt to give an introduction to this important circle of ideas.

Place: 77201

Time: Nov. 22 3:30pm-4:30pm

The Bloch-Beilinson Conjectures are some of the deepest open questions in mathematics today, relating aspects of algebraic geometry, algebraic K-theory and number theory.

The conjectures have roots, on the one hand, in classical results (Euler, Riemann, Dedekind, Hilbert, Artin, etc.) on special values and zeroes of zeta functions, in the period upto the early 20th century.

Another source, somewhat more recent (going upto the mid 1970's) is work of Tate, Iwasawa, Lichtenbaum, Quillen and Borel, which brought in the role of algebraic K-theory.

The most recent inspiration, beginning with several key calculations of Bloch, relate these to algebraic geometry. Bloch's vision was articulated in a general, more precise form by Beilinson, around 1982, resulting in what we now call the Bloch-Beilinson Conjectures. There are also refinements (e.g. the Bloch-Kato conjectures).

In fact there is tantalising, but rather meagre, evidence to support these conjectures, inspite of some 30 years of effort by mathematicians.

My lecture will attempt to give an introduction to this important circle of ideas.