# Arithmetic Geometry, Motives and Number Theory

The study of algebraic varieties and their properties is vast and heterogeneous: one approach is the one given by motives (both Grothendieck’s and Deligne’s, but also by Voevodsky, Morel and Nori) and by the study of the arithmetic properties through Hodge theory, Shimura varieties, as well as L-functions and Iwasawa’s theory.

Specific subjects are

*- *p-adic Hodge theory, Shimura varieties and Torelli locus, Deligne 1-motives (Fabrizio Andreatta).

*- *Motives (a la Grothendieck, Deligne, Voevodsky, Nori, etc.) versus homotopical algebra and Hodge theory (Luca Barbieri-Viale).

- Elliptic curves, modular forms, L-functions, Iwasawa theory, higher dimensional cycles (Massimo Bertolini).

- Motives (after Grothendieck, Voevodsky, Morel, etc.), finiteness notions and Bloch’s conjecture on surfaces, K-theory (Carlo Mazza).

- Selberg's class and automorphic functions, transcendence problems, and exponential sums (Giuseppe Molteni).

- Arithmetic of abelian varieties, p-adic L-functions, Heegner points and Stark-Heegner points (Marco Seveso).

**Keywords**

Hodge theory, 1-motives, motives, L-functions, K-theory

**Pubblications**

Andreatta, Fabrizio, Coleman-Oort's conjecture for degenerate irreducible curves. Israel J. Math.187 (2012), 231–285.

Mazza, Carlo, Voevodsky, Vladimir ; Weibel, Charles: Lecture notes on motivic cohomology. Clay Mathematics Monographs, 2.American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2006. xiv+216 pp. ISBN: 978-0-8218-3847-1; 0-8218-3847-4

Molteni Giuseppe, Representation of a $2$-power as sum of $k$ $2$-powers: the asymptotic behavior, Int. J. Number Theory v.8 n.8, 1923--1963 (2012) (PDF)

## COMPONENTS

Members from the Department of Mathematics | ||
---|---|---|

Fabrizio ANDREATTA | info | |

Luca BARBIERI-VIALE | info | |

Massimo BERTOLINI | info | |

Carlo MAZZA | info | |

Giuseppe MOLTENI | info | |

Marco SEVESO | Postdoc | info |