ICTS:30184

Video URL

Applied l-adic cohomology, I (RL 4)

Applied l-adic cohomology, I (RL 4)

(2024). Applied l-adic cohomology, I (RL 4). SciVideos. https://youtube.com/live/vdCxbYBEPfc

Applied l-adic cohomology, I (RL 4). SciVideos, Oct. 31, 2024, https://youtube.com/live/vdCxbYBEPfc 

          @misc{ scivideos_ICTS:30184,
            doi = {},
            url = {https://youtube.com/live/vdCxbYBEPfc},
            author = {},
            keywords = {},
            language = {en},
            title = {Applied l-adic cohomology, I (RL 4)},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30184 see, \url{https://scivideos.org/icts-tifr/30184}}
          }
Philippe Michel
Talk numberICTS:30184
Source RepositoryICTS-TIFR
Source EventCircle Method and Related Topics
Collection

Abstract

The notion of congruence (modulo an integer q) was formalised by C. F. Gauss in his Disquisitiones arithmeticae. This is a basic yet fundamental concept in all aspects of number theory. Indeed congruences allow to evaluate and compare integers in way considerably richer than the archimedean order alone permits.

In analytic number theory, several outstanding question -starting with Dirichlet’s theorem on primes in arithmetic progressions- reduce to the of measuring whether some classical arithmetic function (say the characteristic function of prime numbers) correlate with suitable q periodic functions for instance Gauss sums, Jacobi sums or Kloosterman sums. It turns out that these functions, when the modulus q is a prime (to which one can reduce via the Chinese Reminder Theorem) can be recognised as « trace functions». The study of trace functions was initiated by A. Weil in the 1940’s and was pursued by A. Grothendieck in the second half of the century with his refoundation of alge...