# Questions tagged [schemes]

The first purpose of schemes theory is the geometrical study of solutions of algebraic systems of equations, not only over the real/complex numbers, but also over integer numbers (and more generally over any commutative ring with 1). It was finalized by Alexandre Grothendieck, during the 1950s and the 1960s.

**1**

**1**answer

### Epi-mono factorisations in schemes via scheme-theoretic image

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**1**answer

### Are there nonaffine schemes over which every exact sequence of vector bundles is split?

**1**

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### The weight of a weighted filtration is given (for large $m$) by a polynomial

**3**

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### Do rationally contractible presheaves have rationally contractible injective resolution

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### Closed algebraic subset dominating a curve

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### integral subschems of geometrically integeral schemes

**1**

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### Help to use Statistics and algebra books for community [closed]

**3**

**1**answer

### Extending functors between K-algebras to schemes

**1**

**1**answer

### Intuition behind formal neighborhood and local ring and formal power series

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### Flatness of affine cone due to semicontinuity theorem

**1**

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### Combinatorics of projective planes over commutative rings

**1**

**1**answer

### Relative affine schemes

**5**

**1**answer

### Is every variety an image of a smooth variety?

**8**

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### Ring of global sections of a functor $\mathbf{CRing} \to \mathbf{Set}$

**4**

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### Is the restriction of an injective sheaf on a closed subscheme still injective?

**2**

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### Looking for the exact and the precise statement of Ogus conjecture

**1**

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### Interesting property of a divisor contained in special fiber

**10**

**1**answer

### Motivation for Henselian rings in algebraic geometry

**2**

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### Generalizations of Artin–Verdier duality?

**0**

**1**answer

### Support of a coherent sheaf over a fiber product scheme

**3**

**1**answer

### $H^1(X, GL(n, \mathcal{O}_X))$ and Vector Bundles

**7**

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### Moduli stacks and representability of diagonal by schemes

**6**

**1**answer

### Does Grothendieck's algebraization imply existence of colimits of schemes?

**4**

**1**answer

### Is quotient of projective scheme over arbitrary base by a finite group also projective

**1**

**1**answer

### On the definition of a principal ideal sheaf

**2**

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### Colimits of the infinitesimal neighborhoods of symmetric product in the category of schemes

**2**

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### Foundational question: to nonunitial commutative rings correspond to schemes?

**1**

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### Equidimensional Morphism

**5**

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### How can we generalize the finite type property so that global sections still have the same property?

**2**

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### Is the blowup of a toric variety corresponding to a subdivision normal?

**0**

**0**answers

### Transversally intersecting divisors $C$ and $D$ in a Hartshorne's AG lemma

**0**

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### Quotient of $\text{Proj}(A)$ by the action of a finite group

**5**

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### Colimit of nilpotent thickenings in the category of schemes

**4**

**1**answer

### Vector bundles on complete rings

**4**

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### Reduction theory of higher dimensional algebraic varieties

**3**

**1**answer

### How to show analytification functor commutes with forgetful functor?

**5**

**0**answers

### Curves of genus 0 over a DVR determined by fibers?

**7**

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### What is the category of coherent sheaves on a logarithmic scheme?

**2**

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### A Subfunctor of Quot-functor compatible with pullbacks

**2**

**0**answers

### Rank of the top Chow group

**1**

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### Valuation diagram of scheme

**5**

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### Is an algebraic space having a monomorphism to an affine scheme a scheme?

**-1**

**1**answer

### Finiteness of the integral closure of an integral domain in its field of fractions

**1**

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### Gluing categorical limit over subgraphs

**4**

**0**answers

### Gluing two affine schemes along a different intersection

**34**

**2**answers

### Building algebraic geometry without prime ideals

**2**

**0**answers

### etale locally infinitesimal lifting property

**1**

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### Existence of integral extension of DVR satisfying some conditions

**1**

**1**answer

### Fpqc-locally constant if and only if étale-locally constant?

**3**

**2**answers