Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Algebraic Geometry (2021/2022)
The teaching is organized as follows:
Learning outcomes
The goal of the course is to introduce the basic notions and techniques of algebraic geometry including the relevant parts of commutative algebra, and create a platform from which the students can take off towards more advanced topics, both theoretical and applied, also in view of a master's thesis project. The fist part of the course provides some basic concepts in commutative algebra, such as localization, Noetherian property and prime ideals. The second part covers fundamental notions and results about algebraic and projective varieties over algebraically closed fields and develops the theory of algebraic curves from the viewpoint of modern algebraic Geometry. Finally, the student will be able to deal with some applications, as for instance Gröbner basis or cryptosystems on elliptic curves over finite fields.
Program
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MM: COMMUTATIVE ALGEBRA
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This first part of the course provides an introduction to commutative algebra, covering topics such as localization, spectrum of a ring and Noetherian property.
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MM: METHODS OF ALGEBRAIC GEOMETRY
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This second part of the course builds upon the commutative algebra introduced in the first part in order to study fundamental results about algebraic varieties over algebraically closed fields. The last part of the course will focus on elliptic curves and their fundamental role in modern cryptography. More precisely, we will study how they can be used to implement key exchanges and digital signatures.
Bibliography
Examination Methods
The exam consists of an oral examination. Each student may choose to either: 1. carry out a traditional oral examination on the contents of the course; or 2. present a topic chosen in agreement with the course coordinators. One additional point will be awarded to those students who achieve 50% or higher in the weekly exercise sheets.
